stress strain curve research papers

A Compact System for Accurate Measurement of True Stress-Strain Curves in Transparent Materials Subject to Extensive Deformation

17 Pages Posted: 26 Sep 2023

Zhenning Chen

Nanjing University of Aeronautics and Astronautics

Xinqiao Tang

Huatao zhao.

Accurate quantification of the true stress-strain curve over an extensive strain range is pivotal for elucidating material mechanical properties and simulating non-linear plastic deformation. A novel experimental approach was developed to directly measure true stress-strain behavior in transparent materials. Our setup featured a single 3CCD camera and a mirror, capturing images of both specimen surfaces with bicolored fluorescent speckle patterns. Initially, we determined and corrected the specimen’s refractive index using a point-by-point least squares method. Subsequently, we used multispectral dual 3D digital image correlation (DIC) to reconstruct surface profiles and correct refractive distortions. This allowed precise computation of the deformed cross-sectional area over an expansive strain range. True stress was calculated from the measured engineering stress and computed deformed area. Validity was confirmed by deforming a fluorescent elastomer, and results aligned with the theoretical predictions. This compact experimental setup effectively evaluates true stress-strain relationships in transparent materials under extensive deformation.

Keywords: digital image correlation, large strain, true stress-strain curve, transparent materials

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Zhenning Chen (Contact Author)

Nanjing university of aeronautics and astronautics ( email ).

Yudao Street 210016 Nanjing,, 210016 China

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Measurement of short span stress-strain curves of paper

• Warren J. Batchelor and Bo S. Westerlind

© 2018 by Walter de Gruyter Berlin/Boston

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The Stress Strain Curve of Paper

The explanation of the in-plane tensile stress-strain curve of paper has long been a matter for debate. In an earlier study it was shown that the elastic modulus of paper is given by an equation Ep = aφEf, where a is a function of the orientation distribution of the fibres in the sheet, φ describes the efficiency of stress transfer between them, and Ef is the elastic modulus of the fibres. As a result of extensive work on the effect of various paper-making treatments on the stress-strain response of paper, we have now shown that the plastic regime can be described in a similar manner, that is to say, in terms of the visco-elastic properties of the fibres, the orientation factor, and the efficiency factor. It is concluded that the non-linear behaviour of the stress-strain curve of paper originates primarily from the properties of the component fibres and not from the sheet structure.

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Determination of the Actual Stress–Strain Diagram for Undermatching Welded Joint Using DIC and FEM

Nenad zoran milošević.

1 Innovation Center of Faculty of Mechanical Engineering, Belgrade University, 11000 Belgrade, Serbia; sr.ca.gb.sam@civesolimm (M.M.); sr.ca.gb.sam@civeralsama (A.M.)

Aleksandar Stojan Sedmak

2 Faculty of Mechanical Engineering, Belgrade University, 11000 Belgrade, Serbia; sr.ca.gb.sam@kamdesa (A.S.S.); sr.ca.gb.sam@cikabg (G.M.B.); sr.ca.gb.sam@civonedalmg (G.M.)

Gordana Miodrag Bakić

Vukić lazić.

3 Faculty of Engineering, University of Kragujevac, 34000 Kragujevac, Serbia; sr.ca.gk@cizalv

Miloš Milošević

Goran mladenović, aleksandar maslarević, associated data.

The data presented in this study are available on request from the corresponding author. The data are not publicly available due to [ongoing research].

This paper presents new methodology for determining the actual stress–strain diagram based on analytical equations, in combination with numerical and experimental data. The first step was to use the 3D digital image correlation (DIC) to estimate true stress–strain diagram by replacing common analytical expression for contraction with measured values. Next step was to estimate the stress concentration by using a new methodology, based on recently introduced analytical expressions and numerical verification by the finite element method (FEM), to obtain actual stress–strain diagrams, as named in this paper. The essence of new methodology is to introduce stress concentration factor into the procedure of actual stress evaluation. New methodology is then applied to determine actual stress–strain diagrams for two undermatched welded joints with different rectangular cross-section and groove shapes, made of martensitic steels X10 CrMoVNb 9-1 and Armox 500T. Results indicated that new methodology is a general one, since it is not dependent on welded joint material and geometry.

1. Introduction

The tensile diagram, commonly used in practice, is called engineering stress–strain diagram, with both stress and strain defined with respect to the initial, cross-section A 0 and gauge length l 0 . For many engineering problems this approximation is good enough, because stresses and strains are close to their true values, as long as contraction and plastic strains are not significant. Anyhow, in the opposite case, true stress–strain diagram is a better option. In its simplest form, true stress and strains are defined as follows, [ 1 ]:

where σ t and ε t denote the so-called true stress and strain, respectively, F is the acting normal force, A current cross-section, which takes into account the contraction, Δ l elongation, l current referent length, l = l 0 + Δ l , l 0 initial length, while σ eng and ε eng denote engineering stress and strain, respectively. It should be noted that terms true stress and strain are used here to emphasize the difference with respect to engineering stress and strain, and should not be understood literally. As a matter of fact, modifications of these equations have been in the focus of many researchers for the past few decades.

To start with, based on the fact that contraction is not the only contribution to true stress, couple of other formulas have been proposed, like the formula for equivalent true stress, as defined by Bridgman, [ 2 ]:

where C B is the correction factor:

with a and R representing the ligament and the radius of curvature at the site of contraction.

The same approach is used by Ostsemin [ 3 ], with a different correction factor C O :

In [ 3 ], a procedure is suggested for calculating the correction for neck formation for round and plane specimens made of homogeneous material. Other correction factors were used in [ 4 ] for deriving equivalent stress–strain curve with axisymmetric notched tensile specimens, with experimental verification and good agreement with the Bridgman correction at large strains. Another approach is based on equivalent strain, as defined by Scheider [ 5 ]:

leading to:

By measuring the mean value of axial strain, formula for the true stress was obtained, [ 5 ]:

One should notice that homogeneous material with rectangular cross-section was analyzed in [ 4 , 6 ], where the tensile properties of FH550 and X80 steels were investigated using rectangular cross-section specimens with different thicknesses, respectively.

Tensile diagrams for welded joints have been determined in [ 7 ], using novel methods for determining true stress–strain curves for homogenous materials with rectangular cross-section and weldments with round cross-section. In the first case, the relation between the total area reduction and the thickness reduction was derived, consisting of three parts—geometry function, material function, and basic necking curve. In the latter case the central idea was to force plastic deformation at a notch in the material zone of interest, and to obtain the true stress–strain curve of that material zone from the recorded load versus diameter reduction curve.

The same topic was considered in [ 8 ], but for different shape of welded joint, the so-called tailor-welded blank weldment. It was concluded that the predicted strain distributions were in good agreement with the measured ones, thus demonstrating the validity of the proposed experimental method to accurately determine the true stress–strain values of the weldment.

More conventional, notched cross weld tensile testing for determining true stress–strain curves for weldments was considered in [ 9 ], whereas a method for determining material’s equivalent stress–strain curve with any axisymmetric notched tensile specimens without Bridgman correction was considered in [ 10 ]. Further in [ 11 ] the stress–strain relation for the weld metal is determined through experimental investigations of round tensile specimens. The true stress–strain curve was developed by using the modified version of the weighted average method. Yet another overmatched welded joint was considered in [ 12 ], where mechanical behavior with planar type laminations in the base metal (BM), heat-affected zone (HAZ), and welding bead (WB) was studied. By using HV data, an equivalent true stress–strain curve in the HAZ was estimated, based on corresponding hardness value obtained from the BM and WB. In [ 13 ] a method to determine the mechanical properties for the weldment of two dual phase (DP) steels is discussed. Inverse numerical simulation was used to simulate the indentation tests to determine and verify the parameters of a nonlinear isotropic material model for the weldment. Results are presented for tensile tests on smooth, notched, and notched-welded specimens. It was shown that the yield and tensile strengths of the notched specimens are higher than the strength of the smooth specimens of the base material due to the additional notch stresses. Similar research is presented in [ 14 ], where the microstructure, macro and micro-mechanical properties of dissimilar A302/Cr5Mo were investigated by metallographic experiments, tensile and nanoindentation tests. Based on inversion analysis, elastoplastic properties were estimated for parent metal, weld metal, as well as fine and coarse grain heat-affected zones.

In neither case, presented here, material heterogeneity of a welded joint was not taken into account if a weldment cross-section was rectangular at the same time. The only such a case known to these authors is the welded joint with true stress–strain curves obtained in a special iterative procedure for all local zones (base metal—BM, weld metal—WM, heat-affected zone—HAZ), have different properties, as shown in a series of papers, [ 15 , 16 , 17 ]. Anyhow, the iterative procedure presented in [ 15 , 16 , 17 ] is not an option here, since it does not lead directly to the result and requires both numerical analysis and experimental testing, not only to verify numerical results, but also to obtain them.

Here, attention is focused to the so-called undermatched welded joint, meaning that the yield stress is lower in a weld metal than in a base metal. One should notice that the plastic strain in undermatched weld metal will appear even with relatively low level of loading, not only due to lower yield stress, but also due to stress concentration, as shown in [ 18 , 19 ]. Once plastic strain becomes significant, cross-section is changed and contraction becomes important, although not the only factor affecting the stress increase. Namely, as it will be shown in this paper, the stress concentration is equally important for this analysis. Therefore, we will use the term actual for the stress–strain diagram exclusively for the case when the stress concentration is taken into account, in addition to contraction.

Toward this aim, one important issue tackled here is the true stress evaluation, which is based on Equation (1), and on contraction values measured by using DIC. As it is shown in this paper, there are significant differences between analytical and measured values of contraction, leading to different true stress–strain curves. For that reason, the term true stress–strain curve is used here for curves obtained by using DIC, whereas the curves obtained by using Equation (1) only are referred to as “true” stress–strain curves. Taking this difference into account, the actual stress–strain curves, as presented here, are based on true stress–strain curves obtained by using DIC, and finally, corrected for the stress concentration.

One should notice that this procedure is a general one, since it will be shown that it does not dependent on welded joint materials and geometry, so it can be applied to overmatched welded joints, as well. Anyhow, since the contraction and plastic strain in that case will be shifted to the base metal, there is almost no practical interest for such an analysis from the point of view of welded joints.

In this work the actual stress–strain diagrams of undermatched welded joints with rectangular cross-section, made of martensitic steel X10 CrMoVNb 9-1 and martensitic armored steel Armox 500T are determined. The goal was to check if different levels of undermatching and different shapes of cross-section, as well as different geometry of welded joint, affect actual stress–strain curve, determined by using formulas proposed in this paper. During the experiment, strains were measured in three dimensions using 3D DIC and software Aramis, to evaluate contraction of rectangular cross-section, i.e., to calculate the current cross section of a specimen, so that true stress–strain diagram can be obtained. Finally, correction for the stress concentration is made, using analytical expressions introduced in [ 20 ] and verified by comparison with the results of finite element analysis, but only in the case of one material (Armox 500T) and one geometry (specimen P1-1).

Manuscript structure, after the introduction, comprises materials and methods, results, discussion, and conclusions.

2. Materials and Methods

Rectangular test specimens are made of martensitic steel X 10CrMoVNb 9-1 (1.4903–by EN 10216) cut from a pipe, and martensitic steel Armox 500T (SSAB, OxelÖsund, Sweden), cut from a plate. In both cases, a combination of TIG and MMA welding process was used for pipe and plate welding. In both cases S Ni 6082 (EN ISO 18274) was used as filler material for the root and hot pass, and filler material E 19.12.3 Nb R 26 (ISO 3581) was used for filling passes. Chemical compositions of base and filler metals are shown in Table 1 and Table 2 , respectively.

Chemical compositions of base metals.

Chemical compositions of the filler metals.

From Table 1 it can be concluded that the base metals used, although both of martensitic microstructure, have significantly different chemical compositions. This is the case because the martensitic microstructure is not obtained in the same way. For 1.4903 steel, martensite was achieved by alloying and consequent heat treatment, whereas for Armox 500T increased carbon content was used, as well as the heat treatment. Materials will not behave in the same way under loading, and this can be concluded by comparing the mechanical properties presented in Table 3 for the base metals and in Table 4 for the filler metals. Materials with different mechanical properties are used to find out if undermatching level affects the proposed formula for stress evaluation. Namely, as one can see from Table 3 and Table 4 , the undermatching coefficient, defined the ratio between weld metal and base metal yield stress (R p0,2 ), is significantly different, circa 0.9 for steel 1.4903 (400/450) and circa 0.32 (400/1250) for Armox 500T.

Mechanical characteristics of the base metals (BM).

Mechanical characteristics of the filler metals (FM).

Test specimens were made with “V” joint for 1.4093 steel and with “X” joint for Armox 500T, as shown in Figure 1 . Dimension ratios for C1 specimens (steel 1.4903) are 8/10 = 0.8, and for P1 specimens (Armox 500T) are 7.4/7.5 = 0.99, which is practically square. Different shapes of the specimen cross-sections and grooves are also used to find out eventual effects of welded joint geometry on the proposed formulas for stress evaluation.

Dimensions [mm] of the specimens for steel 1.4903 (C1) and for Armox 500T (P1).

Digital image correlation (DIC) is a powerful non-contact technique for measuring surface displacement/strain fields, [ 21 ]. Simple geometric shapes can be treated by 2D analysis, while more advanced, 3D analysis, should be used for more complex geometric shapes, including welded joints, as applied and presented in [ 22 , 23 , 24 ]. The force during the experiment was controlled by strain, with the rate 2 mm/min. Setup of the experiment with the position of cameras is shown in Figure 2 . Using DIC method with two cameras (3D deformation measurement) and the Aramis software (Version 2M, GOM GmbH, Braunschweig, Germany) the current cross-section area can be determined. Accuracy of this method for strain measurement is very high, in order of micrometers, so it is a suitable method for the experiment performed here.

Setting up an experiment with the position of the cameras and with the extensometer set.

Finite element method (FEM) is nowadays a widely accepted numerical tool to get stress and strain distribution for many engineering problems, including elastic-plastic analysis of welded joints, even in the presence of cracks, and for other complex problems, [ 25 , 26 ].

Here, 3D FEM is used to evaluate stress concentration. Mesh was made with 3D linear elements, C3D8, with 8 nodes, with decreasing size in the weld metal down to 0.4 × 0.2 mm, as shown in Figure 3 , where one example of meshes deformed in weld metal is given. One quarter of specimen was modeled due to two planes of symmetry and appropriate boundary conditions applied (one rotation and two translations fixed). Load is defined as the negative pressure, according to the force applied and remote cross-section. More detailed description is given in [ 20 ].

FE model of specimen P1-1 with deformed weld metal.

Typical result for strain measurement by DIC is shown in Figure 4 , as obtained by the post-processing, using software Aramis.

Analysis of changes in the characteristic dimensions of the specimen C1-1.

The current cross-section area of the specimen was calculated using data obtained by Aramis, as shown in Figure 5 for specimen P1-1. One of the sides was actually measured, the opposite one taken as the mirror image, and two remaining are obtained by rotating the measured one for 90° and −90°.

Initial (marked by line) and final (green) cross-section area of specimen P1-1.

Figure 6 shows three stress–strain diagrams for both specimens, types C1 and P1, including engineering diagram, obtained by standard tensile test, marked in black. Remaining two diagrams represent true stress–strain curves, one determined according to Equations (1) and (2), marked in red, and the other one determined using measured cross-section areas of the specimen by DIC, marked in blue. One can see that the true stress is increased, if contraction measured by DIC ( Figure 5 ) is taken as relevant. This is why red curves in Figure 6 are marked as “true” and blue ones as true.

Comparison of true and engineering diagrams calculated by DIC method.

Results of FEM calculation are shown in Figure 7 for specimen C1-1 as an example of the procedure applied. Results for C1-1 specimen, with deformed weld metal according to strains and contraction obtained by DIC, show equivalent stress distribution, Figure 7 a, and normal stresses distribution, Figure 7 b, for the applied load 4 KN, producing remote tensile stress 100 MPa in the narrow part of the specimen, away from the welded joint area.

Stress distribution in specimen C1-1 with deformed weld metal: ( a ) equivalent stresses, ( b ) normal stresses, given in MPa.

From Figure 7 it can be concluded that the difference between maximum Misses equivalent stress and maximum normal stress is just 3.91 MPa (215.9–212 MPa) or 1.84%. This leads to the conclusion that the equivalent stress is not the dominant parameter for stress increase, but it is rather the stress concentration due to contraction. To calculate the actual stress with the stress concentration taken into account, the authors propose the following equations:

where C NM is the stress concentration factor and σ T is calculated as:

Stress concentration factor C NM can be separated into two factors, as follows:

where C zs takes into account the welded joint geometry and C EP stands for reduction of thickness. According to [ 22 ], C zs can be expressed for point 1, as follows:

where b 1 and R 1 are defined in Figure 8 for two characteristic points in a weld metal, together with their counterparts, b 2 and R 2 , used for calculating C zs for point 2.

Characteristic dimensions of weld metals: ( a ) V shape, ( b ) X shape.

Likewise, C EP can be defined as, [ 22 ]:

where t 0 and W 0 are initial values of thickness t and width W , Figure 8 . Therefore, the final expression for the stress concentration factor is:

The current cross-sectional area of the specimen ( A current ) was calculated using the data obtained by the DIC.

In the further analysis, numerical verification of coefficients for specimens C1-1 and P1-1 is shown for strains immediately before the fracture:

• Specimen C1-1

• Specimen P1-1

The values obtained in ABAQUS for the quarter of the specimen C1-1 and P1-1 at the characteristic points (1 and 2) are shown in Figure 9 . Stress for specimen C1-1, the maximum equivalent stresses (von Misses) are:

Maximum equivalent stresses in MPa at the characteristic points for specimens: ( a ) C1-1, ( b ) P1-1.

For specimen P1-1, the maximum equivalent stresses (Misses) by Abaqus are:

The equivalent stress values, obtained by ABAQUS and the stresses calculated by the formulas (10)–(15), are given in Table 5 . One should notice difference between stress values in points 1 and 2 for specimen C1-1 and almost the same stress values in these two points for specimen P1-1.

Comparison of the maximal stresses for the specimen C1-1 and P1-1.

In Figure 10 and Figure 11 , actual, true, and engineering stress–strain diagrams are presented for the specimen C1-1 and for the specimen P1-1, respectively.

Actual stress–strain diagrams for the specimen C1-1.

Actual stress–strain diagrams for the specimen P1-1.

4. Discussion

In this research the new methodology for true stress–strain curves are applied to undermatched welded joints made of different base metals, with different geometries (cross section and groove shape). One should notice that both base metals, used in this research, are low plasticity materials, especially Armox 500T (elongation A = 8%). Therefore, using only Equations (1) and (2) for determining the true stress–strain diagram produced questionable result, since the force drop is followed by the stress drop, as shown in Figure 6 for both base metals. Thus, the real contraction, as measured by 3D DIC, should be also taken into account, providing more realistic true stress–strain curves for both base metals, also shown in Figure 6 . As already mentioned, at this stage of development, one side of the specimen was actually measured, and the opposite one taken as the mirror image, while the remaining two sides are obtained by rotation. Anyhow, this issue will be tackled in future work by using at least four cameras to measure the two sides, and get the other two as mirror images. Measuring all the sides is probably too complicated, but it will be considered, as well.

Anyhow, in addition to previous, stress concentration due to geometry change should also be taken into account. Toward this end, new analytical expressions, i.e., formulas (10)–(15) have been introduced in the scope of this research, and verified by using the FEM. This was enabled by using results for strains and contraction, as obtained by DIC, to form FE models with different geometries of weld metal for different load levels, as explained in more detail in [ 20 ] using one base metal and one welded joint geometry. Here, this methodology is applied to both base metal and welded joint geometries to investigate eventual effects on actual stress–strain curves.

From Figure 10 and Figure 11 one can see that actual stresses σ max 1 actual and σ max 2 actual differ in specimen C1-1, while in the specimen P1-1 they are almost the same. Clearly, this is the effect of joint shape, since V joint (specimen C1-1) has different dimensions b 1 and b 2 , and thus different radii of curvature R 1 and R 2 , leading to different stress concentration factors, as well. For the specimen P1-1, difference between σ max 1 actual and σ max 2 actual is negligible due to the symmetry of joint shape (X), having approximately same values of b 1 and b 2 , and radii of curvature, R 1 and R 2 , leading to almost the same stress concentration factors.

It is also important to notice that differences in stresses calculated by the proposed formulas (10)–(15) and equivalent stresses obtained by Abaqus for the moment immediately before the fracture, Figure 9 , do not exceed 4.10% (specimen C1-1, Table 5 ). With this in mind, it can be considered that the proposed formulas evaluate the actual stress correctly for different levels of undermatching and different types of weld groove, as well as different shape ratio of the specimen cross section. Therefore, it was proved here that the proposed methodology is a general one, and can be applied to different materials and welded joint geometries.

One should notice that these effects are important for undermatched welded joints, since only in this case plastic strain and stress concentration develop in the weld metal, contrary to the overmatching welded joint, where they shift to the base metal, i.e., out of the critical zones of welded joint. Anyhow, it is still important to analyze overmatching effect in future research, since it is the most often case in practice.

5. Conclusions

The proposed Equations (10)–(15) proved to be sound basis to determine the actual stress–strain diagrams for undermatching the welded joints made of different base metals with different welded joint geometries. Actual stresses obtained by these formulas are in good agreement with the equivalent stresses obtained by Abaqus using finite element meshes constructed according to the geometry obtained by DIC.

It can be concluded that the actual value of the tensile strength of a welded joint is far above the value obtained by the standard tensile testing, presented by engineering stress–strain curves. This difference is a consequence of cross-section contraction and stress concentration in the most deformed zone, being the weld metal in the case of undermatched welded joint.

Cross-section contraction turned out to be an important factor in the case of low plasticity material, as used in this research, since the usual formulas for “true” stress–strain curves provide questionable behavior with drop of stress after maximum tensile force is reached.

The differences in normal and equivalent stress in rectangular specimens are not significant, leading to the conclusion that the dominant effect in rectangular specimens is not triaxial stress state, but the stress concentration due to contraction.

Further analysis should use more ductile material to analyze their behavior with respect to cross-section contraction and stress concentration, as well as other types of welded joints, such as overmatching joints and different welded joint geometries, to suggest eventual corrections to the proposed formulas.

Author Contributions

Conceptualization, N.Z.M. and A.S.S.; methodology, N.Z.M.; software, N.Z.M. and M.M.; validation, N.Z.M., A.S.S. and G.M.B.; formal analysis, N.Z.M. and A.S.S.; investigation, N.Z.M.; resources, V.L., M.M. and G.M.; data curation, N.Z.M., A.S.S.; writing—original draft preparation, N.Z.M.; writing—review and editing, A.S.S. and N.Z.M.; visualization, N.Z.M., A.S.S. and A.M.; supervision, A.S.S. and G.M.B. All authors have read and agreed to the published version of the manuscript.

The results presented are part of a research supported by MESTD RS by contract 451-03-9/2021-14/200105.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Data availability statement, conflicts of interest.

The authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

• DOI: 10.1016/0008-8846(73)90096-3
• Corpus ID: 136515762

A numerical approach to the complete stress-strain curve of concrete

• S. Popovics
• Published 1 September 1973
• Engineering, Materials Science
• Cement and Concrete Research

1,782 Citations

Generic form of stress-strain equations for concrete, an improved analytical constitutive relation for normal weight high-strength concrete, complete generalization of the equations for the stress–strain curves of concrete under uniaxial compression.

• Highly Influenced

A mathematical model for the prediction of damage in concrete

A mathematical model for complete stress-strain curve prediction of permeable concrete, non-linear analysis of the bond strength behavior on the steel-concrete interface by numerical models and pull-out tests, unified stress–strain model of concrete for frp-confined columns, total strain theory and path - dependence of concrete, nonlinear simulation of stress-strain curve of infill materials using plp fit model, analysis of reinforced concrete shells with transverse shear forces, one reference, a stress-strain function for concrete subjected to short-term loading, related papers.

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What Is the Stress-Strain Curve?

Learn more about how a stress-strain curve helps determine a material's behavior.

A stress-strain curve is a graphical depiction of a material’s behavior when subjected to increasing loads. Stress is defined as the ratio of force to cross-sectional area, while strain is defined as the ratio of the change in length of a dimension to the dimension’s original length. Stress-strain curves can be generated to investigate a material’s behavior when any type of load (tensile, compression, shear, bending, torsion) is applied. We will, however, will focus solely on the stress-strain curves generated by tensile loads. Stress-strain curves generated for tensile loads are important because they enable engineers to quickly determine several mechanical properties of a material including: modulus of elasticity (Young’s modulus), yield strength, ultimate strength, and ductility. A stress-strain curve is obtained by conducting a tensile test (a type of test where a load is continuously applied to a test specimen until it fractures). The stress experienced by the part is graphed on the Y-axis, while the strain is graphed on the X-axis. This article will define the stress-strain curve, its different regions, how to interpret it, and its importance to material selection.

.css-2xf3ee{font-size:0.6em;margin-left:-2em;position:absolute;color:#22445F;} .css-14nvrlq{display:inline-block;line-height:1;height:1em;background-color:currentColor;-webkit-mask:url(https://assets.xometry.com/fontawesome-pro/v6/svgs/light/link.svg) no-repeat center/contain content-box;mask:url(https://assets.xometry.com/fontawesome-pro/v6/svgs/light/link.svg) no-repeat center/contain content-box;-webkit-mask:url(https://assets.xometry.com/fontawesome-pro/v6/svgs/light/link.svg) no-repeat center/contain content-box;aspect-ratio:640/512;vertical-align:-15%;}.css-14nvrlq:before{content:"";} What Is Stress?

Stress is the amount of force applied to a cross-sectional area. It’s a highly important calculation because it allows engineers to quantify the amount of force that a material can tolerate before fracturing. This parameter is used by engineers to select materials and designs that will result in safe, durable structures. The formula for stress is shown below:

Stress formula.

• 𝜎 is the stress
• F is the applied force
• A is the cross-sectional area. 

The SI unit for stress is the Pascal (Pa), but pounds per square inch (psi) is also commonly used.

What Is Strain?

Strain is defined as the deformation experienced by a material relative to its original dimensions. Strain, like stress, is an essential calculation because it helps engineers quantify how much deformation a material can accommodate before it permanently deforms or fractures. The formula for strain is defined below: 

Strain formula.

• ε is the strain
• Lf is the final length
•  L0 is the initial length

Strain is a unitless value since the numbers in both the top and bottom of the formula are in units of length.

How Is the Stress-Strain Curve Measured?

Fortunately for all of us, stress-strain curves are generated automatically by modern tensile testing machines. These machines continuously monitor and record the force applied to a test specimen and the amount of deformation it experiences as a result of that load. The most commonly used test methods for tensile testing and creating standardized stress-strain curves are those issued by ASTM International. ASTM E8 standardizes tensile tests for metallic materials while ASTM D638 standardizes tensile tests for plastic materials. The steps to creating a stress-strain curve are described in the list below:

• Prepare the test specimen to the required dimensions.
• Mount the test specimen in the jaws of the tensile testing machine.
• Apply a continuously increasing tensile load to the specimen until it breaks.
• The tensile testing machine will record the stress and strain experienced by the test specimen based on readings of force applied by the load cell and displacement of the jaws holding the test piece.

The Different Types of Stresses and Strains

There are two types of stresses and strains that are described in detail below:

1. Engineering Stress and Strain

Engineering stress and strain are the stress-strain values of material calculated without accounting for the fine details of plastic deformation. These values are also referred to as nominal stress and strain. The values for engineering stress and strain are convenient for measuring the performance of a material and can be directly obtained from a standard tensile test. The formula for engineering stress is shown below:

Engineering stress formula.

Where A0 is the original cross-sectional area of the test specimen. The SI unit for stress is the Pascal (Pa), but pounds per square inch (psi) is also commonly used. 

The formula for engineering strain is given below:

Engineering strain formula.

Strain is a unitless measurement.

2. True Stress and Strain

True stress and strain are the actual stress and strain experienced by a material while taking into account its deformation during a tensile test. It is ideal for analyzing the mechanical properties of a material. True stress and strain must be calculated from experimental data related to the test specimen’s instantaneous gauge length, cross-section area, and applied load throughout the test. The formula for true stress is shown below:

True stress formula.

Where Ai is the instantaneous cross-sectional area. The formula for true strain is shown below:

True strain formula.

Where Li is the instantaneous length.

Stages of the Stress-Strain Curve

A stress-strain diagram has three stages. In the first stage, the material experiences only elastic deformation. When the applied stress is released, the material returns to its original dimensions. 

Uniform plastic deformation takes place in the second stage. This stage begins at the yield point and continues for as long as the material can continue to strengthen through strain hardening (the same process that occurs in cold forming) with every new increment of the applied load. Eventually, the material's capacity for stable plastic deformation is exhausted. The amount of plastic strain that can be tolerated during this phase tells us a lot about the material's relative brittleness or ductility.

The final stage of a tensile test is referred to as “necking.” This stage occurs after the material’s ultimate tensile stress is reached, and no further strain hardening is possible. Instead of continued, stable deformation, a region of localized deformation forms somewhere in the cross-section of the test specimen. The excessive tensile stresses reduce the material’s dimensions that are perpendicular to the applied force which causes a significant reduction in area. This makes the material have the shape of a “neck”. Once necking begins, the engineering stress of the material decreases while the true stress continues to increase.  The material fractures soon after necking begins. The stress-strain curve is shown below.

How To Read the Stress-Strain Graph

The general steps for how to read a stress-strain graph are described below:

• Pick a stress value on the Y-axis.
• Trace a horizontal line from the Y-axis until it intersects the stress-strain curve’s line. 
• Mark the point where the horizontal line and stress-strain curve line intersect.
• Trace a vertical line down from the intersection point to X-axis. The two traced lines should form a sharp, 90° corner.
• The stress value chosen from step 1 shows the stress that corresponds to the strain, or deformation, experienced by the test specimen at that point.

The steps above can be used to determine the strain experienced by the test specimen at the moments the yield stress, ultimate tensile strength, and fracture point are reached.

The Different Regions of the Stress-Strain Curve Graph

Five significant points can easily be picked off a stress-strain curve. The interpretation of each point offers unique insight into the mechanical behavior of a material. The five points are described in detail below:

1. Proportional Limit

The proportional limit refers to the point at the end of the linear portion of the stress-strain curve. All of the deformation up to the proportional limit occurs with one proportionality constant, called Young's modulus. It is calculated as the slope of the line (stress divided by strain) up to the proportional limit. In this region, Young’s modulus can be obtained by calculating the slope of the line. 

2. Elastic Limit

The elastic limit is the observed point on the stress-strain curve where elastic deformation ends and plastic deformation begins. When the applied load is released at any point up to the elastic limit, the material will regain its starting dimensions. In metals, the elastic limit is often difficult to distinguish from the proportional limit and the yield point since the points on the curve are so close to each other. Therefore, the elastic limit is more often used for educational purposes rather than actual characterization of a material’s properties.

3. Yield Point

The yield point is similar to the elastic limit of the stress-strain curve in that it also describes the point where elastic deformation ends and plastic deformation begins. The primary difference between the two is that the yield point is a calculated value that precisely describes the elastic limit, or yield strength of the material. The yield point is determined by offsetting the linear portion of the stress-strain curve by +0.2% along the horizontal (strain) axis. The intersection point of the offset line with the original stress-strain curve is considered the yield strength of the material.

4. Ultimate Stress Point

The ultimate stress point, or ultimate tensile strength, is the highest stress observed on the stress-strain curve. After the ultimate tensile strength is reached, the test specimen begins to “neck.” It’s important to note that while the ultimate stress point is the highest point observed on the stress-strain curve, the actual highest stress is actually the true stress at fracture.

5. Fracture or Breaking Point 

The fracture or breaking point is the point on the stress-strain curve where the test specimen has deformed so much that its microstructure gives and the part fractures.

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Stress-strain relationship of high-strength steel (HSS) reinforcing bars

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Reinforcement strength, ductility and bendability properties are important components in design of reinforced concrete members, as the strength of any member comes mainly from reinforcement. Strain compatibility and plastic behaviors are mainly depending on reinforcement ductility. In construction practice, often welding of the bars is required. Welding of reinforcement is an instant solution in many cases, whereas welding is not a routine connection process. Welding will cause deficiencies in reinforcement bars, metallurgical changes and recrystallization of microstructure of particles. Weld metal toughness is extremely sensitive to the welding heat input that decreases both of its strength and ductility. For determining the effects of welding in reinforcement properties, 48 specimens were tested with 5 different bar diameters, divided into six groups. Investigated parameters were: properties of un-welded bars; strength, ductility and density of weld metal; strength and ductility reduction due to heat input for bundled bars and transverse bars; welding effect on bars' bending properties; behavior of different joint types; properties of three weld groove shapes also the locations and types of failures sections. Results show that, strength and elongation of the welded bars decreased by (10-40%) and (30-60%) respectively. Cold bending of welded bars and groove welds shall be prevented.

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Reinforced concrete is a versatile, economical, and proven construction material. Able to be placed to a variety of shapes and finishes, it is durable and strong, performing well throughout its service life. However, the corrosion of steel reinforcement in an aging highway infrastructure is a major problem currently facing the transportation engineering community, in particular bridge engineers. Use of Micro-composite Multi-structural Formable Steel, commercially known as “MMFX”, as a replacement for convention steel is gaining popularity in many concrete structures. The high-corrosive resistance nature and high-strength characteristics of the MMFX rebars can provide additional service life to concrete structures in areas that are prone to severe environmental conditions. Despite the extensive research efforts, which have been conducted to date, there is little guidance available for practicing engineers on the use of high-strength and high-performance steels as flexural reinforcements of concrete beams. The research program presented in this thesis was of multi phases to examine the mechanical characteristics of the MMFX steel, evaluate their corrosion resistance, investigate and assess their structural performance as main flexural reinforcement using typical full-scale T-section concrete beams reinforced by MMFX rebars. The research presents the experimental program carried out at the Reinforced Concrete Structures laboratory at Ain Shams University, Cairo, Egypt. Eight full-scale concrete beams were constructed and tested. All beams were T-section of 500 mm flange width by 80 mm thick. The web was 250 mm wide by 400 mm deep. The nominal length of all beams was 4000mm. Six beams were reinforced by MMFX rebars in the tension side while the remaining two beams were reinforced by conventional steel rebars Grade (40/60) in the tension side. The beams were equally reinforced by conventional steel rebars Grade (40/60) on the compression side except for the beam with maximum reinforcement ratio. All beams were tested under static loading conditions up to failure in order to investigate the pre-cracking, cracking, post-cracking behavior as well as ultimate capacities and modes of failure. Deformations, strains in longitudinal reinforcement, and crack pattern were recorded during the test at different loading stages. In the second phase of the research program, a comprehensive analysis of the tested specimens was conducted using cracked section analysis. The predicted behavior was compared to that observed during testing. All MMFX reinforced concrete beams experienced higher ultimate strength and a comparable amount of ductility in comparison to beams reinforced by conventional steel rebars (Grade (40/60)). The failure mode of most beams was classified as ductile flexural failure accompanied by yielding of the tension reinforcement preceding the crushing of the concrete. Only two beams failed due to rupture of the MMFX rebars. One more beam exhibited shear failure. No bond failure was observed during testing. The design recommendations and guidelines are proposed based on the results of this investigation and additional parametric study that was conducted in light of the experimental results. Based on the research findings, the minimum and maximum reinforcement ratio has been identified as well as the optimal use of MMFX as flexural reinforcement for concrete structures.

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Poly(lactic acid) (PLA)/poly(butylene succinate adipate) (PBSA) films with Micro fibrillated cellulose (MFC) and cardanol for packaging applications

• Original Research
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• Published: 31 August 2024

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• Annalisa Apicella 2 , 3   na1 ,
• Giovanna Molinari 1 , 2 , 4   na1 ,
• Vito Gigante 1 , 2 ,
• Arianna Pietrosanto 3 ,
• Loredana Incarnato 2 , 3 ,
• Laura Aliotta 1 , 2 &
• Andrea Lazzeri 1 , 2  

Micro Fibrillated Cellulose (MFC) has emerged as a promising component in film formulations due to its unique barrier prope.rties. In this study, to best of our knowledge, cardanol, a biobased plasticizer derived from cashew processing, was employed for the first time, as a dispersing aid for MFC, during a liquid assisted extrusion technique with a Poly(lactic acid) (PLA)/Poly(butylene succinate adipate) (PBSA) blend. The aim of the work is the production of PLA/PBSA/MFC films for packaging applications. The addition of different MFC amount was investigated (added at 0.5, 0.75 and 1 wt.% concentrations). The results obtained are very interesting, in fact from one hand Cardanol improved the compatibility between PLA and PBSA and avoided the MFC agglomeration. On the other hand, micro fibrillated cellulose ensured a stable film blowing and the achievement of enhanced barrier properties, seal ability and mechanical resistance. In particular, the best result was obtained with an MFC content of 0.75 wt.% for which a good compromise in terms of films ductility, barrier properties and seal ability was achieved.

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Introduction

For many years fossil-based polymers have been widely used in the packaging industry for different applications (films, pouches, rigid and foamed containers, etc.). However, growing fears on the environmental impact of the fossil-based polymers as well as the necessity to decrease the greenhouse gas emissions, has forced researchers and the industry to develop more sustainable packaging (Stark and Matuana 2021 ; Malafeev et al. 2023 ). In this context the use of biobased materials coming from renewable resources has gained much interest (Zinoviadou et al. 2016 ). Particular attention has been dedicated to find more sustainable solution in the packaging field due to its large plastic consumption (de Sousa 2021 ). The movement towards more sustainable packaging solution requires the development on novel biobased materials together with the improvement of the existing ones (Dörnyei et al. 2023 ).

Among the biobased polymers, poly(lactic acid) (PLA) is the most attractive, being also available on the market with different grades customized for different structuring processes (Swetha et al. 2023 ). Although PLA exhibits good mechanical strength, printability and transparency, its barrier properties to gases and water vapor, ductility, processability and thermal stability are usually lower than conventional fossil-based plastics and fail to fully meet the demanding standards of many flexible packaging applications, among others, for food and beverages preservation (Apicella et al. 2018 ; Leneveu-Jenvrin et al. 2021 ; Samir et al. 2022 ; De Luca et al. 2023 ). The overcoming of PLA drawbacks can further widespread its application not only in the packaging sector (Qian and Sheng 2017 ).

At this purpose, to improve the PLA toughness and ductility, a possible strategy could be the reactive extrusion to develop block or random copolymers in melt compounding (Augé et al. 2023 ), or converting polymer blends into in situ composites through the formation of well-aligned micro/nanofibrils by virtue of such an external field, permitting the construction of strong dispersed phase and interfacial interaction (Evstatiev and Fakirov 1992 ; Xie et al. 2014 ). Nevertheless, an efficient low-cost technique, commonly adopted at industrial level, is the physical blending through twin-screw extrusion with a more ductile polymer (Nofar et al. 2019 ). Among the biodegradable and biobased polymers commercially available, the most interesting one, to be blended with PLA for flexible packaging applications, is the poly(butylene succinate co-adipate) (PBSA) (Aliotta et al. 2023a ; Mastalygina and Aleksanyan 2023 ). Indeed, the PBSA good eco-efficiency coupled with its high availability, flexibility, excellent impact strength, as well as thermal and chemical resistance and good biodegradability (Changwichan et al. 2018 ) makes it an excellent candidate for the blending with PLA, as also demonstrated by a recent work in which extrusion processing parameter have been optimized with a DoE approach for the production of these blends (Gigante et al. 2023 ). Indeed, different successful studies can be found regarding the good flexibility reached with PLA/PBSA blends (Pivsa‐Art et al. 2015 ; Lascano et al. 2019 ; Suwanamornlert et al. 2020 ; Aversa et al. 2022 ; Aliotta et al. 2023a ). Therefore, PBSA is an excellent candidate to improve the PLA flexibility especially when its content is around 40 wt.%. For this PBSA content in fact, an improvement of the elongation up to 200% also accompanied by an increase in impact resistance three times higher than that of pure PLA have been reported (Aliotta et al. 2021 ).

Nevertheless, in some cases it is also necessary to improve the barrier properties and to reach this goal the use of suitable filler is necessary (Botta et al. 2021 ; Nath et al. 2023 ).

Cellulose can be used as filler to improve not only the barrier properties but also the mechanical ones (Kalia et al. 2011 ; Dufresne 2017 ). In particular, the unique properties of micro fibrillated cellulose (MFC) (high specific strength and modulus, high aspect ratio, light weight, low cost, biodegradability, and renewability) makes it very attractive to reinforce polymeric matrices (Li et al. 2021 ). The main issues to be faced on, are related to MFC drying, the incompatibility of hydrophilic cellulose and hydrophobic polymer matrices and the MFC agglomeration. In fact, being MFC generally produced in aqueous suspension, its drying leads to an irreversible agglomeration. Furthermore, it must be considered that the use of MFC suspensions during melting compound requires an efficient water removal to avoid the degradation of water sensible polymers (van den Oever et al. 2010 ; Lamm et al. 2021 ). An industrial sustainable technique to guarantee the MFC dispersion within the polymeric matrix and an efficient water removal, is the liquid assisted extrusion with the help of suitable plasticizer as MFC dispersing aids (Clemons and Sabo 2021 ). The incorporation of a suitable plasticizer into the MFC suspension has been proved to be a good solution to guarantee the MFC dispersion and at the same time to improve the processability. In literature several plasticizers have been successfully adopted like lactic acid oligomers (OLA), poly(ethylene glycol) (PEG), Triethyl citrate (TEC) (Paul et al. 2021 ; Molinari et al. 2021 ; Völtz et al. 2022 ; Aliotta et al. 2023b ). However, the low molecular weight of these plasticizers can generate problems related to the plasticizer migration (Marcilla et al. 2017 ).

For the first time, the use of cardanol oil (CA) (derived from the side product of the cashew agro-industry) as MFC dispersing aid was investigated. The molecular structure of cardanol oil make him less prone to its migration from the polymeric matrix (Mele et al. 2019 ). Cardanol is constituted by a mixture of phenolic compounds (Bloise et al. 2012 ) and thanks to the presence of the C15 chain attached to the meta-position of the phenolic ring, cardanol and its derivatives possess a relatively high solubility in non-polar environments and good processability. In addition, it has been observed that CA addition to a PLA matrix by hot melt extrusion has led to good results in terms of mechanical performance and processability (Hassouma et al. 2016 ; Greco et al. 2018 ; Mele et al. 2019 ). Moreover, it has been demonstrated that the cashew nut-derived oils can exert antioxidant and antibacterial properties (Andrade et al. 2011 ; Boonsai et al. 2014 ; Anand et al. 2015 ) making the use of CA oil more attractive.

In this work the attention was focused on the production and characterization of novel PLA/PBSA films containing different MFC amount (0.5–0.75 and 1 wt.%) and CA as dispersing aid. Based on previous studies of the same research group (Aliotta et al. 2021 , 2023a ) the ratio between the PLA/PBSA in the matrix was 60/40 (60 wt.% of PLA and 40 wt.% of PBSA), chosen based on the good ductility reached by this blend. The biocomposite were obtained by using the well-established wet extrusion compounding technique (Clemons and Sabo 2021 ) in which an emulsion containing MFC ana CA was fed. The optimization of the temperature and venting of the extruder zones was carried out to achieve a complete water stripping. Subsequently the granules obtained with different MFC content, were again processed through film blowing technique and the obtained films were characterized from a morphological, mechanical, and thermal point of view. Then, by considering the possible applications of the obtained films for packaging sector, the barrier properties, contact angle and film seal ability were also explored.

Materials and methods

The materials used in this work are:

Poly(lactic acid) (PLA), trade name Luminy LX175, purchased from Total Corbion PLA (Gorinchem, Netherlands). It is an extrusion grade PLA coming from natural resources having about 4% of D-lactic units [density:1.24 g/cm 3 ; melt flow index (MFI): 6 g/10 min at 210 °C and 2.16 kg).

Poly(butylene succinate-co-adipate) (PBSA), trade name BioPBS FD92PM, purchased from Mitsubishi Chemical Corporation (Tokyo, Japan), is a copolymer of succinic acid, adipic acid and butandiol. This PBSA grade is tailored for both blown and cast film extrusion [density of 1.24 g/cm 3 ; MFI: 4 g/10 min at 190 °C and 2.16 kg].

Cardanol (CA) NC-514, provided by Cardolite (Gent, Belgium): is a di-functional glycidyl ether epoxy resin having a good reactivity. The chain of 8 carbons separating the aromatic groups allows to increase the flexibility processability [Epoxy Equivalent Weight: 490; viscosity at 25 °C: 25,000 cPs; density at 25 °C: 8.75 g/cm 3 ].

Micro Fibrillated Cellulose (MFC), trade name Exilva F 01-L 10%, provided by Borregaard (Sarpsborg, Norway) with a solid content of 1.5–2.4% (viscosity—in H 2 O 2wt.%—≥ 14,000 mPa·s). These MFC are constituted by long and thin fibers arranged in a three-dimensional net- work interconnected to each other (Molinari et al. 2021 ).

Preparation of the MFC/plasticizer emulsions and composites

To avoid the MFC agglomeration, cardanol was used as dispersing aid. An emulsion with cardanol, water and MFC was prepared to be fed into the extruder thank to the liquid assisted extrusion technique adopted with success in previous works (Molinari et al. 2021 ; Aliotta et al. 2023b ). The procedure adopted for the liquid assisted extrusion consists of several steps as follows:

Distilled water was added to MFC, despite their initial dilution, to obtain H 2 O/MFC solutions at 2 wt%.

Cardanol was added to the previous dilution to achieve four different emulsions with the following (H 2 O/MFC/CA) ratios by weight: (89.5/0.5/10), (89.25/0.75/10) and (89/1/10).

The emulsions were then mechanically stirred with an IKA T 25 digital ULTRA-TURRAX® Disperser (Staufen, Germany). The stirring was carried out at 8000 rpm for 210 s to disperse and homogenize the CA with the MFC. The emulsions obtained were stable and does not show phases separation.

The stable mixed emulsions were then fed through peristaltic pump in proximity of middle length of the twin-screw extrusion system. PLA and PBSA granules in a 60/40 ratio were fed into the extruder through the main feeder located at the beginning of extruder length. The extruder, equipped with a vacuum pumping system that can remove, during the extrusion, the water present in the emulsions, just leaving the plasticizer, MFC and the polymeric PLA/PBSA matrix. A PLA/PBSA matrix with 60 wt.% of PLA and 40wt.% of PBSA was chosen due to its good compromise between processability and mechanical properties (Aliotta et al. 2021 , 2023a ).

The extrusion compounding was carried out with a semi-industrial COMAC EBC 25HT (L/D = 44) twin-screw extruder (COMAC, Cerro Maggiore, Italy). The formulations produced and their relative compositions are reported in Table  1 .

The vacuum pump was positioned in proximity of the end of the extruder length to guarantee the maximum stripping yield. The profile temperature adopted along the 11 extruder zones was: 150/170/180/180/180/180/180/190/190/185/180 °C using a mass flow rate of 2.5 kg/h and a screw speed of 100 rpm. The strands coming out from the extruder were cooled in a water bath and then pelletized by an automatic cutter.

FT-IR characterization

To evaluate any eventual interaction between the PLA/PBSA matrix, cardanol and MFC, ATR spectra were recorded on the extruded granules for each blend. The characterization was carried out at room temperature in the 500–4000 cm −1 range using a Nicolet 380 FT-IR spectrometer (Thermo Fisher Scientific, Madison, WI, USA) equipped with a smart iTX ATR accessory.

Rheological characterization of the blends

The dynamic rheological properties of PLA_PBSA, 10C, 10C_0.5MFC, 10C_0.75MFC and 10C_1MFC blends granules were assessed by the rotational ARES rheometer (Rheometric Scientific, New Castle, Delaware, USA), in oscillatory mode from 0.1 to 100 rad/s at 185 °C, using a parallel-plate geometry (diameter = 25 mm). The analyses were conducted under nitrogen atmosphere on the granules dried at 70 °C for 12 h in vacuum oven, to prevent moisture degradation. A strain amplitude of 5% was set to ensure the linear viscoelastic regime. The tests were carried out in triplicate yielding a standard deviation below 2%.

Film blowing

Before the film blowing the blend granules were vacuum dried at 70 °C for 12 h. Single layer blown films were produced using a Gimac film blowing unit featuring a single screw extruder (D = 12 mm, L/D = 24), a spiral mandrel die for blow film (with inner and outer diameters of 30 and 30.5 mm, respectively), and a take-up/cooling system. The films were extruded setting the temperature profile equal to 185/185/175/160 °C, the blow-up ratio (BUR) equal to 2.5 and the collection speed at 1.6 m/min, yielding to samples with an average thickness equal to 45 ± 3 µm. The extrusion proved successful for all the blends compositions except for the 10C sample, which exhibited challenges during blown film processing due to bubble instability. A picture reporting the film processing and the different film formulations produced is reported in Fig.  1 .

Film blowing and related films produced for this work

The film morphologies and MFC dispersion were observed by FEI Quanta 450 FEG scanning electron microscope (SEM) (Thermo Fisher Scientific, Waltham, MA, USA). The samples for SEM analyses were cryo-fractured under liquid nitrogen. To avoid some electrostatic charging effects, due to the interaction between the electron beam and the polymeric materials, all the samples were firstly sputtered with a thin layer of platinum by means of LEICA EM ACE 600 High Vacuum Sputter Coater (LEICA, Wetzlar, Germany).

Mechanical characterizations

On the films obtained by film blowing, several mechanical tests were performed. For each test typology, at least five specimens for each formulation were tested.

Tensile tests were carried out on an Instron universal testing machine model 5500R (Canton, MA, USA) equipped with a 100 N load cell interfaced with Merlin software (INSTRON version 4.42 S/N–014733H). Compressed air grips were used to clamp the film specimens. The specimens consisted of strips having rectangular shape (80 mm length and 15 mm width). The initial grip separation was 50 mm, and the deformation rate was set at 50 mm/min. From this test the final stress and elongation at break of the films was calculated.

The elastic modulus was determined by dynamic mechanical analysis (DMA) carried out on a Gabo Eplexor (Gabo, Ahlden, Germany), equipped with a 100 N load cell. Rectangular specimens were used (gauge length: 20 mm; width: 4 mm). During the test the temperature and the frequency were kept constant and equal to 25 °C and 1 Hz respectively.

The critical tearing energy of the films was evaluated through trouser tear tests carried out with the above mentioned INSTRON universal testing machine.

Trouser tear tests according to the ASTM D1938-02 were carried out at a crosshead speed of 250 mm/min. The “legs” of the trouser specimens were pulled in opposite direction to create a tearing force (mode III of fracture) (Andreasson et al. 2013 ; Islam et al. 2019 ). The load and extension values were recorder during the test and the critical tearing energy was calculated as follows:

where F is the maximum peak load recorded during the test and B is the film thickness.

Tear test at high-speed was carried out thanks to Elmendorf test, a very common test carried out on blown and cast films (Kissin 2011 ). An Elmendorf pendulum (MESDAN, Puegnago del Garda, Italy) with a weight of 1.6 kg was used and the ISO 6383 was applied to calculate the maximum tearing force. The tests were carried out at room, and the maximum tearing force, in Newton, was registered at higher speeds (50,000 mm/min).

Thermal characterizations

To verify any modification of the thermal properties due to the addition of CA and MFC, calorimetric analysis was performed using a TA-Q200 DSC (TA-Instruments, New Castle, DE) equipped with an RSC cooling system. Indium was used as a standard for the DCS calibration while nitrogen, set at 50 ml/min, was used as purge gas. About 10–15 mg of material, cut from the blown films, was sealed within aluminum hermetic pan. To evaluate the crystallinity reached by the films after the film blowing, only the first heating run was considered. The following thermal program was adopted: heating from 0 at 10 °C/min up to 190 °C. The melting temperature ( T m ) and the cold crystallization temperature ( T cc ) were recorded as the maximum of the melting peak and the minimum of the cold crystallization peak respectively. The enthalpies of melting (Δ H m ) and cold crystallization (Δ H cc ) were calculated integrating the areas under the corresponding peaks. The PLA and PBSA crystallinity ( X cc ) were calculated according to Eq.  2 (Aliotta et al. 2021 ), where ∆ H m and ∆ H cc are the melting and cold crystallization enthalpies respectively. ∆ H ° m is the theoretical melting heat of 100% crystalline polymer and it is equal to 93 J/g for PLA (Fischer et al. 1973 ) and to 142 J/g for PBSA (Bureepukdee et al. 2015 ).

Oxygen and water vapor barrier characterizations

Oxygen permeability tests were conducted on the films in triplicate, following the ASTM D1434-82 standard, by a GDP-C gas permeabilimeter (Brugger, Munich, Germany) at 23 °C, 10% RH, under an oxygen flow rate of 80 mL/min and at a pressure differential of 1 bar. Permeability coefficients (P O2 ) were calculated by multiplying the oxygen transmission rate by the thickness (mm) of each film.

Water vapor permeability measurements were carried out in triple, according to the ASTM F 1249–90 procedure, by a 7002 WP-Permeation Analyzer (Systech Illinois, Princeton, NJ, USA) at 23 °C and 50% RH. Water vapor permeability coefficients (P H2O ) were determined by multiplying the water vapor transmission rate values obtained by the thickness (mm) of each film.

Contact angle measurements

Films wettability was evaluated following the ASTM D5946 standard by static water contact angle measurements, using an FTA 1000 Analyzer (First Ten Angstroms, Inc., Portsmouth, VA, USA) with 2 ± 0.5 µL drop volume and at least ten replicate measurements.

Seal ability characterization

The films sealing ability was assessed according to the ASTM F1921-98, Method B procedure by hot tack tests, using an HSG-C heat seal tester (Brugger, Germany. The welds were performed on 15 mm-width film strips, applying 0.3 N/mm 2 sealing pressure and 1 s welding time, in the T range from 70 °C, corresponding to the initiation sealing temperature, to 85 °C, above which the film undergoes excessive warping.

Optical properties

The transparency of the films was evaluated with Cary 60 UV–Vis Spectrophotometer (Agilent Technologies, Santa Clara, USA), by measuring the Transmittance % of visible light at 550 nm, according to the ASTM D1746-03 standard.

The color of the films was assessed by colorimeter (CR-4100 Chroma Meter, Konica Minolta, Japan) and the results were expressed according to CIELAB colour coordinates L* (darkness/lightness), a* (greenness/redness), b* (blueness/yellowness). The colour-difference with respect to the PLA_PBSA film was evaluated using the equation ΔE* ab , following the standard ASTM D2244.

Results and discussion

Rheological results.

Prior to carry out the film blowing process, the blends processability was preliminary investigated by rheological oscillatory analyses. Figure  2 displays the plots of the complex viscosity η* (a) and storage modulus G’ (b) for PLA_PBSA blends, while the zero-shear viscosity values are outlined in Table  2 . As noticeable from Fig.  2 a, all samples exhibit a shear-thinning behavior; the most pronounced is that of the PLA_PBSA matrix, which also shows the highest values of complex viscosity throughout the investigated frequency range.

Complex viscosity curves a and storage modulus curves b of the PLA_PBSA blends

The addition of cardanol to the polymer matrix (sample 10C) results in a substantial decrease in viscosity: in particular, this sample shows the lowest values of η* in the entire ω range, while the zero-shear viscosity value (η 0 *), with respect to the PLA_PBSA blend, drops from 6039 to 3581 Pa s.

The decrease in complex viscosity after cardanol oil addition is a typical plasticizing effect. Cardanol acts as plasticizer increasing the free volume and chains mobility of the polymer matrix, as also reported by other authors in literature (Alexander and Thachil 2006 ; Greco et al. 2019 ; Mele et al. 2019 ; Ali et al. 2020 ).

With respect to the 10C sample, the MFC addition in the blend induces an increase in viscosity. Specifically, for samples loaded with 0.5% and 1% MFC (i.e., 10C_0.5MFC and 10C_1MFC, respectively), only a slight increase in complex viscosities is observed, and the η 0 * values increase from 3581 Pa s, for the 10C sample, to 3735 and 3818 Pa s for the 10C_0.5MFC and 10C_1MFC samples, respectively. On the other hand, the sample loaded at 0.75% MFC (i.e., 10C_0.75 MFC) exhibits the largest increase in viscosity (η 0 * equal to 4595 Pa s) and a more pronounced Newtonian plateau, while at high strain rates (i.e., at high ω values) the complex viscosity approaches that of the neat resin.

These results suggest that the rheological behavior of the composites is strongly correlated to the MFC concentration and its degree of dispersion and distribution in the polymer matrix and can be also interpreted considering SEM analyses, which will be discussed in detail later in the article. In particular, the small viscosity increases in the case of 10C_0.5MFC sample may be associated with a low MFC content coupled with a poor filler distribution as highlighted by SEM analyses. The rheological behavior of sample 10C_0.75MFC suggests that higher interactions between the filler and the polymer matrix were achieved, thanks to a better dispersion and distribution of the filler in the PLA_PBSA matrix. Further increase in MFC percentage up to 1% may induce a worsening in the dispersion and distribution of the filler in the polymer resin, leading to lower complex viscosity values with respect to the 10C_0.75MFC sample.

These observations are also reflected in the storage modulus (G') curves (Fig.  2 b). The presence of 10 wt.% of cardanol, plasticizes the matrix causing the highest decrease in the elastic component, which is relevant in the film extrusion process. For samples loaded with MFC, at low strain rates, and therefore for long relaxation times, the plots of G' overlap. At high strain rates, instead, the storage modulus curve of sample 10C_0.75MFC overlaps with that of the neat PLA_PBSA matrix.

Based on the rheological data, the film blowing process was carried out. For sample 10C, the presence of the plasticizer alone made the blown filming process unstable, and it was not possible to collect the film. On the other hand, the enhanced melt elasticity introduced by MFC presence, particularly for concentrations equal to 0.75wt. % and 1 wt.%, ensured a stable film blowing process.

Mechanical and morphological results

The trends of the main mechanical properties (elastic modulus, stress at break and elongation at break) with the overlap of significant stress–strain curves are reported in Fig.  3 .

Mechanical results and relative main stress–strain curves

The mechanical results of PLA/PBSA matrix are in accordance with the literature (Yang et al. 2019 ; Aliotta et al. 2023a ). The addition of the more ductile PBSA phase allows the obtainment of flexible film having an elongation at break of around 300%. As it could be expected, the addition of the MFC rigid phase, has led to an increment of the film elastic modulus with the MFC content. A slight decrement of the stress at break with MFC content was observed; however, this decay is not so marked with values of stress at break that are comparable to the PLA/PBSA matrix. The mechanical results obtained, are in accordance with other studies (Suryanegara et al. 2009 ; Uribe et al. 2016 ; Jesus et al. 2022 ) that ascribed the stiffness increment and the decrement of stress end elongation at break to the presence of the rigid MFC phase. Interesting is to observe the trend of the elongation at break. In fact, even if a decrement of the film’s ductility was registered for all biocomposites formulations, the addition of MFC has led to an increment of film ductility. This result could be ascribed to the rigid filler toughening effect caused by the MFC addition (Bartczak et al. 1999 ). To reach this toughening effect a proper filler content coupled with good dispersion within the polymeric matrix are fundamental (Wilbrink et al. 2001 ; Argon and Cohen 2003 ). The highest elongation at break was registered for the composite with 0.75 wt.% MFC content in accordance with the rheological behavior. The MFC content to obtain a flexible film seems to be fundamental. This behavior can be ascribed to a bifurcation phenomenon, reported in literature (Argon and Cohen 2003 ), between brittle-like response and ductile response that should occur at a critical filler content. At 0.5wt.% of MFC content a brittle response with poor elongation at break was observed. On the other hand, when the MFC content reached the 0.75wt.% the elongation at break started to increase reaching its maximum value.

The tearing resistance of the films evaluated by different techniques and speeds by trouser and Elmendorf tests are reported in Fig.  4 . It can be observed that the MFC addition improves the films tearing resistance. The MFC presence and its good dispersion limits the crack propagation; in fact, if the filler is homogenously dispersed it can penetrate within polymeric chains and it can limit the slippage of the macromolecules, enhancing the tear resistance (Ismail et al. 2019 ).

Results of Trouser tests (left side) and Elmendorf test (right side)

To confirm the mechanical results, the MFC dispersion was checked by SEM analysis (taken at 5000X) and the micrographs obtained are reported in Fig.  5 . Unfortunately, it was not possible to go to higher magnifications due to the biopolymeric matrix damage caused by the interaction with the electron beam. However, the micrographs obtained allow to confirm the mechanical results.

SEM micrographs at 5000X of a PLA_PBSA film and biocomposites films containing b 10C_0.5MFC, c 10C_0.75MFC and d 10C_1MFC

The addition of the MFC emulsion containing cardanol changes the morphology of the matrix that has a smoother surface; probably this effect can be ascribed to a sort of plasticization (or compatibilization effect) caused by the CA addition. The increasing MFC content can be observed by the “white dots” (having dimensions around 0.2–0.5 μm) which gradually increase in number, going from 0.5 to 1 wt.% of MFC. It can be also observed that at 0.5 wt.% the MFC content is not enough and there are regions in which only matrix is present. This not enough content coupled with a poor filler distribution, is responsible for the decline in elongation at break recorded for this MFC content. Instead, a suitable content and a more uniform distribution of MFC are visible at 0.75 MFC where an improvement in elongation at break and tear resistance were observed. At 1 wt.% the MFC distribution is still good, however are visible white dots with larger dimensions that are ascribable to the MFC agglomeration.

FT-IR results

The FTIR spectra of PLA_PBSA and PLA_PBSA_10C, are reported in Fig.  6 a.

FTIR spectra of a PLA_PBSA and 10C; b PLA10C and 10C with the addition of various MFCs amount

For the PLA_PBSA sample, the peaks at 2933 and 2861 cm −1 corresponds to characteristics stretching vibration of –CH 2 ; while the peaks at 1735 cm −1 and 1174 cm −1 are related to stretching vibration of C=O and C–O, respectively (Palai et al. 2020 ). The peaks at 1443 cm −1 and at 730 cm −1 may be ascribed to C–H and C=C main backbone chain of PLA bending of neat PLA, respectively. Similarly, peaks at 1450 and 1382 cm −1 may be related to bending of O–H bonds of PBSA carboxylic acid group (Bureepukdee et al. 2015 ). The addition of cardanol (10C spectrum), is confirmed by the presence of the peak at 1592 cm −1 , attributable to the C=C stretching vibration present in the aromatic ring of the molecule(Mestry et al. 2021 ). A compatibilization effect of cardanol between PLA and PBSA, is here confirmed through the presence of a 1–2 cm −1 blue-shift between the two spectra displayed in Fig.  6 . This shift can be attributed to the strengthening of the binding energy of the backbone and side groups through inter/intra-molecular interactions (Xie et al. 2016 ). The blue-shift found here would suggest the existence of an enhanced interaction between the two polymers, thus facilitated by the presence of cardanol.

The FTIR spectra of PLA_PBSA_10C with the addition of different amount of MFC, are reported in Fig.  6 b. Here the MFC presence is confirmed by the presence of the peak at 2340 cm −1 , generally attributed to the –N=C=O stretching of the polysaccharide (Kaushik and Singh 2011 ). In addition, it is interesting to notice that as the content of MFC in the sample increases, the area of the peak increases accordingly.

Thermal results

In Fig.  7 and Table  3 are reported the heating thermograms and the results obtained from DSC analysis. The first heating thermograms obtained from DSC analysis, shows the thermal history of the samples produced by film blowing. The analysis of these data was preferred to have a better correlation with mechanical results and barrier results measured on the film specimens.

DSC heating thermograms

A triple melting peak of PBSA, centered at around 83 °C, is observed. The multiple peak melting behavior is typical for PBSA, also noted in other literature works (Wang et al. 2005 ; Aliotta et al. 2021 ). The number of the observable peaks depends on the processing conditions; in fact, according to the melt recrystallization model (Wunderlich 2012 ), the crystallization temperature and the cooling rate affects the crystals formation generating, in some cases, imperfect crystals having lower melting temperature. Moreover, during the melting, the amorphous material could recrystallize into a more perfect crystal having high melting temperature. All these phenomena generate multiple melting peak behavior like those observed for PBSA.

The addition of MFC and CA does not significantly affect the PBSA melting. Contrary to PLA, PBSA does not show cold crystallization, this was mainly ascribed to the very fast crystallization rate of PBSA during cooling that leads to the presence of low amorphous domains able to recrystallize during the heating (Bureepukdee et al. 2015 ). Moreover, the high crystallization rate of PBSA has led to the achievement of crystallinity values (reported in Fig.  7 ) that remain approximately unchanged with and without the MFC presence. It must be pointed out that the PBSA melting peak is partially overlapped with the PLA cold crystallization peak (centered at around 92 °C) making the calculation of the final crystallinity content less accurate; however, it was possible to calculate the formulations crystallinity trend.

With respect to the PLA/PBSA matrix a marked shift of the PLA melting temperature was observed that passed from 150.8 °C in the matrix to around 155.5 °C in the composites systems. This shift can be ascribed to the MFC presence that acts as nucleating agent and facilitates the crystal formation. In particular, the melting peak shift is ascribed to the formation of only one of the two melting peaks associated to PLA. In fact, it is well known from the literature that PLA has a double melting peak associated to the melt/recrystallization of the PLA α form crystals (Righetti et al. 2015 ; Aliotta et al. 2017 ). Depending on the cooling and process conditions, only one or both two peaks are visible. The presence of MFC blurs the peak observed at lower temperatures (recorded for the matrix) and promotes the appearance of a single peak at higher temperatures, consistent with what has also been reported in the literature by Song et al. (Song et al. 2013 ) for PLA/MFC biocomposites.

In Fig.  8 the crystallinity percentages for PLA, PBSA and the sum of them (that is, the total crystallinity of the sample) are reported.

Crystallinity values of the film obtained by film blowing technique

The fast PBSA crystallization led to high PBSA crystallinity values with and without the MFC presence. On the other hand, the PLA crystallinity increases thank to the presence of MFC that act as heterogeneous nucleating agent for PLA. In fact, PLA has a slower crystallization kinetics and, respect to the matrix without MFC, the MFC addition facilitates its nucleation in accordance with literature (Song et al. 2013 ). The best MFC content for which the highest PLA crystallinity, and the total composite crystallinity, was reached was equal to 0.75 wt.%.

Oxygen and water vapor barrier and surface wettability

Oxygen and water vapor permeability tests and contact angle measurements were carried out to investigate possible changes in the barrier and surface properties of the films due to MFC addition in the polymer matrix; the outcomes are displayed in Table  4 . Both the oxygen and water vapor permeabilities of the neat PLA_PBSA sample are at par or lower than literature data reported for films based on PLA/ polybutylene succinate (PBS), PLA/PBSA, PBS/PBSA blends (Yang et al. 2016 ; Bamps et al. 2022 ; Apicella et al. 2023 ; Jariyasakoolroj et al. 2023 ). With respect to the PLA_PBSA sample, the incorporation of different percentages of MFC leads to a decrease in the oxygen permeabilities. This effect must be also correlated to the addition of cardanol as MFC dispersing aid that also act as plasticizer for the polymeric matrix increasing the permeability (Mele et al. 2019 ). However, for samples loaded with 0.5% and 1% MFC only a slight decrease in \({P}_{{O}_{2}}\) values were observed, equal to ca. 4% and 9% for 10C_0.5MFC and 10C_1MFC films, respectively. Conversely, a maximum decrease in \({P}_{{O}_{2}}\) value of 28% was obtained for the 10C_0.75 MFC film. The oxygen barrier results are in close correlation and consistent with the morphological and thermal data discussed before. In detail, the best O 2 -barrier results were found for the 10C_0.75 MFC film, exhibiting a better dispersion and distribution of the filler in the PLA_PBSA matrix and the highest crystallinity degree achieved for both the PLA and PBSA phases. At the same time, the lower decrease in \({P}_{{O}_{2}}\) of the 10C_0.5MFC and 10C_1MFC films could be attributed to the sub-optimal filler concentration, dispersion, and distribution in the composite matrix, as also underlined by rheological analyses.

Regarding the vapor barrier properties, as was to be expected, a slight increase \({P}_{H2O}\) values was observed in the composite structures compared to the pure PLA_PBSA film, with no significant changes with respect to the composition of the films. This is attributable to the inherently hydrophilic nature of MFC due to the high number of hydroxyl groups on its surface, as also reported elsewhere (Jing et al. 2022 ).

Concerning static water contact angle results (Table  4 ), in general, composite films show higher CA w values than the neat PLA_PBSA film; however, this can be reasonably attributed to the presence of the cardanol oil used as a dispersing agent, composed mainly of nonpolar hydrocarbon chains with a phenolic group which makes it relatively hydrophobic. As the concentration of micro-fibrillated cellulose increases, however, the contact angle to water gradually decreases, due to the hydrophilic nature of the filler.

Heat seal performance

The films sealing ability was investigated by evaluating the hot tack strength, namely, the maximum weight the seal can support without breaking, in the temperature range 70–85 °C. The results are displayed in Fig.  9 .

Hot tack curves for the tested films

All the developed films exhibited a seal initiation temperature equal to 70 °C and a temperature of maximum strength equal to 75 °C. In particular, the neat PLA_PBSA film showed the lowest values of hot tack strength in the whole range of temperatures investigated, and a maximum hot tack strength equal to 850 g/15 mm. By increasing the MFC content in the polymer blend, the hot tack strength gradually increased and a maximum hot tack force equal to 900, 925 and 1000 g/15 mm was registered for 10C_0.5MFC, 10C_0.75MFC and 10C_1MFC samples, respectively. This effect can be explained considering that hot tack is a function of interfacial bonding and melt strength and is more influenced by strong molecular forces than cold adhesion. In particular, the ability of micro-fibrillated cellulose to form stronger bonds, such as hydrogen bonds, can induce an improvement of the interfacial adhesion and of the melt strength, leading to an increased hot tack force by increasing MFC concentration (Morris 2017 ; Jarvis 2023 ). It is worth to underline that all the developed films showed a maximum seal strength at T < 100 °C, therefore, they can be suitable for applications in high-speed packaging operations (Bamps et al. 2022 ). What is more, all the films showed maximum seal strength values comparable or higher than those reported in literature for heat sealable, biodegradable films based on PLA, PBS, PBS/PBSA, PLA/polycaprolactone blends (Bamps et al. 2022 ).

The effect of MFC on the transparency and color of the neat PLA_PBSA and of the composite films was evaluated by UV_Vis and colorimetric measurements. Table 5 reports the transmission at 550 nm (T 550 ), the CieLab color coordinates L*, a*, b* and the chromatic variation ΔE* ab for all the films.

As observable, the incorporation of MFC in the PLA_PBSA polymer matrix led to a drop in transparency and a slight increase of the yellowness (b* parameter) and greenness (a* parameter) of the films, whereas the L* parameter remained substantially unchanged. However, no significant changes were noticeable by increasing the MFC concentration from 0.5% up to 1%, and in any case the total color change ΔE* ab of the composite films, evaluated with respect to the neat PLA_PBSA sample, indicate a minimal or imperceptible difference to the human eye under normal viewing conditions (ΔE* ab  ≤ 1).

Conclusions

In this study, biodegradable composite films based on micro fibrillated cellulose were successfully produced by film blowing technique, with the aim to realize a novel structure with improved functional performance suitable for food packaging applications. Different micro fibrillated cellulose (MFC) amount (from 0.5 up to 1 wt.%) was added to the PLA/PBSA matrix, and cardanol oil was employed for the first time as dispersing aid during liquid assisted extrusion.

Cardanol oil was effective in compatibilizing PLA and PBSA and its plasticizing effect substantially decreased the complex viscosity and the storage modulus of the polymer blend, making the film blowing process unstable for the 10C sample. On the contrary, the MFC presence ensured a stable film blowing. Compared to the neat PLA/PBSA sample, the composite films exhibited enhanced oxygen barrier properties, improved hot tack strength without compromising optical characteristics, along with interesting mechanical properties that maintain a good balance between stiffness and ductility. In particular, the 10C_0.75 MFC exhibited a hot tack force equal to 925 g/15 mm and the highest elongation at break (117%) and O2-barrier (P O2  = 13.3 cm 2  mm/(m 2 d bar)), attributable to the best dispersion and distribution of the filler in the PLA_PBSA matrix and the highest crystallinity degree achieved for both the PLA and PBSA phases (28.8% and 30.5%, respectively), which hinder the oxygen permeation.

The results obtained highlighted the close relationship between films processing, morphology and the functional performance achieved, are encouraging and underscore the potential of MFC biocomposites in addressing environmental concerns while fulfilling performance requirements in several industrial applications.

Data availability

The data supporting this study are available when reasonably requested from the corresponding author.

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Annalisa Apicella and Giovanna Molinari have contributed equally to the work.

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Department of Civil and Industrial Engineering, University of Pisa, 56122, Pisa, Italy

Giovanna Molinari, Vito Gigante, Laura Aliotta & Andrea Lazzeri

National Interuniversity Consortium of Materials Science and Technology (INSTM), 50121, Florence, Italy

Annalisa Apicella, Giovanna Molinari, Vito Gigante, Loredana Incarnato, Laura Aliotta & Andrea Lazzeri

Department of Industrial Engineering, University of Salerno, 84084, Fisciano, Italy

Annalisa Apicella, Arianna Pietrosanto & Loredana Incarnato

CNR-IPCF, National Research Council—Institute for Chemical and Physical Processes, 56124, Pisa, Italy

Giovanna Molinari

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L.A.: Conceptualization, Methodology, Formal Analysis, Data curation, Visualization, Writing original draft. A.A.: Conceptualization, Methodology, Formal Analysis, Data curation, Visualization, Writing original draft. G.M.: Investigation,Data Curation, Writing—Review & Editing. V.G.: Methodology, Investigation, Data curation, Validation, Writing—Review & Editing. A.P.: Methodology, Investigation, Data curation, Validation, Writing—Review & Editing. L.I.: Validation, Resources, Supervision, Writing—Review & Editing. A.L.: Validation, Resources, Supervision, Writing—Review & Editing.

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Apicella, A., Molinari, G., Gigante, V. et al. Poly(lactic acid) (PLA)/poly(butylene succinate adipate) (PBSA) films with Micro fibrillated cellulose (MFC) and cardanol for packaging applications. Cellulose (2024). https://doi.org/10.1007/s10570-024-06127-w

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DOI : https://doi.org/10.1007/s10570-024-06127-w

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