Composite Coupons Research Articles

Design and evaluation of a novel variable-length stepped scarf repair technique using a cohesive damage model

The advantages of Carbon Fibre Reinforced Polymers (CFRPs) are well established, but repairing CFRP components remains difficult and costly, posing challenges for industries like aerospace. This paper explores the design, modelling, inspection, and testing of a Variable Length Stepped Scarf (VLSS) repair scheme for highly loaded composite structures. A fully nonlinear 2D Finite Element Model (FEM) is used to design the VLSS repair, predict failure loads and modes, and model adhesive cohesion and delamination. The model incorporates a validated progressive damage model, general contact, and both force and geometric nonlinearities. Two manufacturing techniques involving hard repair patches and glass beads to maintain a constant bond line are employed. A 3D FEM validated against repaired composite coupons under uniaxial tension shows excellent agreement with experimental data. The static strength repair efficiency is approximately 80 % of a pristine sample, with failure displacements at 87 %, and Hooke's stiffness at 102 % of pristine laminates. Cohesive failure at adhesive overlap edges is identified as the cause of stiffness degradation, confirming experimental observations. This study contributes to both composite repair modelling and repair design optimisation.

Response Surface Methodology for Optimisation of Parameter on Water Absorption of Natural Fibre Hybrid Composite in Boat Construction

Today, the utilisation of natural or green fibre has supplanted engineered fibre as fibreglass has become a pattern in composite boat producing and other gears because of its lightweight, excellent relative mechanical properties, and more significant elements. For example, it is eco-accommodating, has manageable materials, and has lower costs compared to fibreglass. The utilisation of fibreglass is costly and has a high effect on the natural biological system. It also gets over the area of ecological contamination, word-related well-being, and security concerns. This study used the Woven Kenaf/fibreglass as reinforcement and polyester as matric to fabricate hybrid composite coupons. Response Surface Methodology (RSM) of Box-Behnken Design (BBD) was applied to optimise fibre contents (35 to 75 wt%) and water absorption performance for the development of Woven Kenaf/fibreglass to polyester hybrid composite material based on the parameters. The BBD revealed that 45% Woven Kenaf/fibreglass to polyester performed the optimum fibre content and water absorption. Analyses of variance (ANOVA) showed that the model satisfactorily correlated the parameters. After immersion, 45% Woven Kenaf/fibreglass to polyester composite also gained 9.48% weight.

Composite Recycling with Biocatalytic Thermoset Reforming.

Carbon fiber reinforced polymers (CFRPs, or composites) are increasingly replacing traditional manufacturing materials used in the automobile, aerospace, and energy sectors. With this shift, it is vital to develop end-of-life processes for CFRPs that retain the value of both the carbon fibers and the polymer matrix. Here we demonstrate a strategy to upcycle pre- and postconsumer polystyrene-containing CFRPs, cross-linked with unsaturated polyesters or vinyl esters, to benzoic acid. The thermoset matrix is upgraded via biocatalysis utilizing an engineered strain of the filamentous fungus Aspergillus nidulans, which gives access to valuable secondary metabolites in high yields, exemplified here by (2Z,4Z,6E)-octa-2,4,6-trienoic acid. Reactions are engineered to preserve the carbon fibers with much of their sizing so that the isolated carbon fiber plies are manufactured into new composite coupons that exhibit mechanical properties comparable to those of virgin manufacturing substrates. In sum, this represents the first system to reclaim a high value from both the fiber fabric and polymer matrix of a CFRP.

Mechanical characterization and performance evaluation of twisted Jute-Kevlar hybrid composites with varied fiber orientations

Abstract Composite materials play a vital role in developing new materials in engineering and technology. Composites show how the properties of the matrix and reinforcement work together to create more robust, more rigid materials than would be possible from the individual components working alone. They consist of two or more component materials combined with notably dissimilar physical or chemical characteristics. Two categories of composite coupons have been developed in this research work: the first category (C1) is made up of jute twisted-Kevlar twisted jute fiber (0/90 degree), and the second category (C2) is made up of jute twisted-Kevlar twisted jute fiber (0/45 degree). The nano-silica is reinforced with the matrix with a weight percentage of 0%,5%,10% and 15%. This involved various mechanical tests, analysis of wear surfaces, as well as DMA, DSC, and FEA testing, and ultimately, the machining of the composites studied. The machining parameters used in waterjet machining have been carefully analyzed. The tensile strength of S3 in category C1 was 163 N mm−2, while S2 in category C2 had 154 N mm−2. The flexural strength of S3 in category C1 was the highest, with 200.23 N mm−2, and S3 in category C2 had 189.32 N mm−2. The impact strength, hardness values having higher than the Category C 2 composites. Overall, the mechanical behaviour of Category C1 exhibits better performance. An increase in reinforcement shows better damping behaviour in DMA study. The performance of up to 10% of nanoparticles was found to be good, in a thermal analysis (DSC). Morphological analysis revealed improper fiber pullout in the developed composites. The material’s wear performance is similar to adhesive wear, with a slight wear loss in the pin on the disc. The machining parameters of the composite showed a relationship between velocity and surface roughness.

Numerical failure modelling of natural fibre composite coupons using X-ray computed tomography based modelling

Natural fibre composites offer versatile applications across industries while being superior in sustainability aspects compared to other composite types. To unlock their full potential, it is essential to understand their complex failure involving fibre failure, matrix cracking, and debonding at the fibre-matrix interface. Efforts to address these challenges focus on advanced numerical models, probing behaviour from micro to macro scales. However, these models face complexities in handling intricate failure modes given the non-uniform nature of natural fibres. To overcome these challenges, image-based modelling using X-ray computed tomography scans is proposed. This work’s novelty lies in integrating detailed microstructure information with a nonlinear calibration procedure to accurately model damage and failure in natural fiber composites. It marks a significant step toward developing a virtual testing model, paving the way for assessing composites with varying fiber content or fiber types.

Vibration-based Damage Diagnosis for a Population of Composite Structures Under Uncertainty via Hyper-Sphere and Transfer Component Analysis Based Methods

The problem of vibration-based damage diagnosis, including the detection and type characterization of damages in a population of nominally identical composite structures under operational uncertainty is investigated. This is an important problem for various types of fleets, such as aircraft, drones, fixed wing UAVs and others, which becomes highly challenging if the variability in the composite materials and the manufacturing of the population is significant, while the diagnosis of early-stage damages is pursued. Such a population of 27 composite coupons subjecting to operating variability due to alterations in the temperature, the excitation and the experimental setup is considered in this study. Furthermore, early-stage delamination and impact-induced damages are implemented in 10 of the coupons. Damage diagnosis is herein attempted via two data-driven methods that may account for various types of uncertainty, which are founded on a number of stochastic Multiple-Input Single-Output Transmittance Function AutoRegressive with eXogenous pseudo-eXcitation (MISO-TF-ARX) models. The first employs Hyper Spheres for the representation of the healthy subspace under uncertainty using the parameters of the MISO-TF-ARX models and thus abbreviated as HS-MISO-TF, while the other is based on the Transfer Component Analysis of these parameters, abbreviated as TCA-MISO-TF. The methods’ damage diagnosis performance is experimentally assessed using the above composite coupons and a high number of 7 500 inspection test cases for damage detection, whereas damage characterization is based on 450 test cases. The damage detection and characterization results are presented through Receiver Operating Characteristics curves and confusion matrices, respectively. The obtained results indicate adequate damage detection with the HS-MISO-TF method to achieve 82.1% correct detection for 5% of false alarms, with the TCA-MISO-TF following with 76.4% correct detection. Damage characterization is remarkable with the HS-MISO-TF to correctly characterizing the considered damage type for the 100% of the considered test cases and the TCA-MISO-TF following with 92.2%.

Glass fibre hybridization to improve the durability of circular flax fibre reinforced composites with off-the-shelf recyclable polymer matrix systems for large scale structural applications

Natural fibre composites (NFCs) are not durable in the long run because of the susceptibility of natural fibres to environmental conditions and specifically moisture. Hybridizing NFC laminates externally, with synthetic fibre reinforcements, may improve durability, due to their inherent environmental resistance. This work aims to investigate the effects of glass hybridization, on flax fibre composites, studied via accelerated ageing. In specific, the durability of hybrid flax/glass fibre reinforced polymer composites, with two recyclable polymer matrices was investigated. Unidirectional (UD) flax and UD glass fibre reinforcements were employed to fabricate laminates, with two fully-recyclable off-the-shelf resin systems, as matrix: (i) a bio-based epoxy resin and (ii) an acrylic liquid thermoplastic (Elium®). In addition, a standard petroleum-based epoxy polymer matrix was for reference purposes. Weathering and hygrothermal ageing were used to test the durability of coupons, exposed to UV radiation/condensation/water spray environment (weathering ageing), and full-immersion in distilled water at 23, 40, and 60°C (hygrothermal ageing). In all cases, ageing was performed for a total duration of 56 days. The performance of the unaged and aged composite coupons was assessed and compared in terms of flexural and viscoelastic performance as well as SEM (Scanning Electron Microscopy) analysis. It was revealed that the addition of glass fibres with flax fibres in the hybrid composites improves the performance and better resistance against ageing environments than their neat flax fibre composites.

Vine copulas for accelerated prediction of composite strength variability

Composite materials are essential for many advanced engineering applications, but numerical quantification of strength variability can be computationally expensive. This paper proposes a novel methodology that drastically reduces the number of finite element simulations required to characterise composite material strength variability using the concept of vine copulas. This concept provides a flexible tool for the representation of high-dimensional dependencies. The methodology considers spatial scatter of three material variabilities: fibre volume fraction, fibre misalignment and fibre strength. First, the cross-correlation between stress, fibre volume fraction and fibre misalignment is fitted by a vine copula using results from a limited number of finite element simulations. Next, the vine copula is used to predict new conditional stress realisations when given realisations for the fibre volume fraction and fibre misalignment. This effectively replaces the finite element simulations with a vine copula that is much faster to evaluate. The methodology is verified by predicting the tensile failure load of a unidirectional composite coupon. Predictions are very similar to an exclusively finite element-based approach, while reducing the number of finite element simulations by a factor of 200.

Multi-metal additive manufacturing of selectively doped 316 L stainless steel-copper composite using hybrid laser powder bed fusion

This paper introduces a hybrid laser powder bed fusion method integrated with material jetting techniques for producing 316 L stainless steel (SS)-copper (Cu) composites. Two molecular Cu precursor inks were formulated and evaluated using two distinct jetting systems: ink jetting and pneumatic jetting. The direct conversion of the Cu precursor ink into metallic Cu was studied using laser scanning, adjusting both laser focus and scan speed. Moreover, factors influencing ink conversion, Cu capture rate, and the effective thermal conductivity of the 316 L SS-Cu system are discussed. The thermal conductivity of both as-printed and annealed composite coupons was observed to enhance by 115% and 181% respectively, when compared to wrought 316 L SS at 300 °C. Microstructural analyses revealed the formation of a continuous Cu network during annealing, which further enhanced the effective thermal conductivity of the composite coupons. The microhardness of the composite coupon decreased by up to 26% compared to wrought annealed 316 L SS. Lastly, the potential of producing multi-metal structures using the hybrid LPBF method is demonstrated.

Finite element simulation of axial crushing of flat and C-channel composite coupons using a modified mesomodel

The present article investigates the axial crushing behavior of IM7/8552 material system. Two types of specimens are considered-(a) flat coupons with saw-tooth trigger and (b) C-channels with 45° chamfer as a trigger. All the crushing test data (load, displacement and velocity history curves) is shared in the Crashworthiness working group (CWG) consortium of the Composite material handbook (CMH17.org). Flat crush coupons are tested at the University of Utah and the C-channels are tested at the John H. Glenn Research Center of the National aeronautics and space administration (NASA). Three types of layups are considered for flat coupons: QI1-[90/±45/0]2S, HL2-[902/02/±45/02] and HL3-[90/45/02/90/-45/02]. Two types of layups are considered for C-channels: HL2-[902/02/±45/02] and HL3-[90/45/02/90/-45/02]. Both the specimens are subjected to crush loading with an initial velocity and lumped mass attached to the impactor. All the ply and interface material properties come from the current authors' testing campaign except for strength and stiffness in the fiber direction. The crushing test cases are simulated in LS-Dyna software. Ply and interface behavior is described via user-defined material subroutines of LS-Dyna software. Each ply is modeled using 3D solid elements and the interfaces are modeled explicitly using cohesive elements. Intraply behavior is described using a novel modified meso model proposed by the present authors. Intraply model accounts for nonlinear damage, plasticity, ply fracture toughness and finite element mesh size. Interply response is modeled using bi-linear law. Predictions from present FE models showed a good correlation with crush test data. The effect of finite element model parameters e.g., filtering frequency, mesh size, interface properties, ply fracture toughness, element erosion criterion, contact stiffness and friction coefficient on crushing predictions is demonstrated by conducting parametric studies.

A vibration-based Machine Learning type Structural Health Monitoring methodology for populations of composite aerostructures under uncertainty

A robust to uncertainty Machine Learning (ML) based Structural Health Monitoring methodology for populations of composite aerostructures is postulated. The methodology is founded upon a number of unsupervised ML algorithms for damage detection and a supervised counterpart for damage characterization. Damage detection is specifically based on two types of Healthy Subspace representations: A Multiple Model (MM) and a varying radii Hyper-Sphere (HS) type. Both are built upon response-only vibration acceleration and/or strain signals at properly selected sensor locations. Based on them, Multiple Input Single Output (MISO) Transmittance Function AutoRegressive with eXogenous (TF-ARX) excitation data driven models representing the partial structural dynamics are obtained. Decision making is then based on the model parameter vector that may be transformed and reduced via Principal Component Analysis (PCA). Damage detection is achieved via multi-level information fusion using acceleration and/or strain sensors. Damage characterization, referring to damage type, location, and level determination, is achieved via a hierarchical cosine similarity based algorithm. The methodology is successfully assessed via hundreds of experiments using a population of small-scale composite coupons for the detection and characterization of Delamination and Impact damage under material/manufacturing, temperature, excitation, and experimental uncertainty.

Bayesian optimization-based prediction of the thermal properties from fatigue test IR imaging of composite coupons

The prediction of the prevailing self-heat transfer parameters of a glass/epoxy composite coupon during fatigue testing in general and the distinction between viscoelastic- and frictional crack growth-related energy dissipation in particular, are not trivial problems. This work investigates the feasibility of predicting the convective film coefficient, the total work loss as well as the ratio between viscoelastic and fracture-induced damping from thermal images using Bayesian optimization in conjunction with 3D FE thermal analysis. To this end, glass fiber/epoxy biax coupons are pre-damaged by means of a drop weight impact machine and subsequently tested under uniaxial tension-tension high cycle fatigue conditions. IR images are taken of the self-heating thermal profile at steady-state conditions. Synthetic surface thermal images are generated by numerical thermal analysis of the damage distribution obtained by μ-CT scanning prior to testing. Bayesian optimization of the aforementioned parameters is conducted by minimizing the loss function between the as-measured and the synthetic IR image. The predicted work-loss is consequently validated against the measured hysteretic response, from which a very good agreement is found.

1 experimental and numerical evaluation of residual mechanical performance of carbon/epoxy laminated coupons after integration of solid battery cells for aeronautical applications

The present study deals with a numerical and experimental evaluation of the residual mechanical performance of a quasi-isotropic carbon/epoxy laminated composite plate in which solid battery cells have been integrated. Firstly, the mechanical properties of the multifunctional Reinforced Multilayer Stack (RMS) battery cells have been determined thanks to dedicated multi-instrumented tests, while those of the AS4/8552 composite material have been extracted from the literature and validated by comparisons with tensile tests on plates without battery, considered as a reference case. Then, on the basis of the recommendations obtained from a virtual test campaign using FE simulations, a 16-ply laminated composite plate containing 6 solid battery cells was manufactured with a modified curing cycle that preserves the electrical properties of the batteries while ensuring the mechanical properties of the composite material. Various control methods, such as CT-scan and optical analysis, were used to demonstrate the promising quality of the manufactured composite coupon with embedded cells. Finally, a mechanical tensile test was carried out to experimentally determine the reduction in mechanical properties. The analysis of such a test with non-linear FE simulation has allowed a better understanding of the damage and failure process when solid battery cells are integrated into high performance laminated composite structures designed for the aeronautical industry.

Automated bondline thickness quantification in adhesively joined composites and metals using ultrasound

AbstractThe use of adhesively bonded joints between composite panels, metal panels, or between composites and metals are used in the aerospace and automotive industries to avoid stress concentrations due to fasteners while reducing weight. Quantifying the bond thickness allows for confidence that loading is being properly transferred. This study presents a methodology to measure bondline thickness using the data obtained from an immersion quality ultrasound scan using an out‐of‐tank, field‐portable, utlrasonic testing (UT) scanner. Eighteen bonded coupons were fabricated using a paste‐type adhesive filling a range of gaps between substrates of 0.254 and 1.27 mm. Three adhesively bonded coupon types were investigated: carbon fiber laminates, fiber glass laminates, and aluminum plates. A semiautomated algorithm is presented to quantify bondline thickness from the ultrasound data for each coupon type, generating a spatially varying 3D point cloud of adhesive thickness. Bondline measurements obtained using ultrasound are then validated over two orthogonal planes against measurements taken from x‐ray computed tomography reconstructions. Results indicate a typical accuracy of 0.081 mm for bondline thickness quantification for all samples studied, with the results from the inspection of the composite coupons yielding an error of 0.078 mm, whereas the accuracy when scanning the aluminum coupons yielded an error of 0.086 mm.Highlights Field‐portable, inspection station is presented for full waveform ultrasonics. Mathematical procedure to characterize adhesive bondline thickness. Results are presented for a variety of material systems and adhesive thicknesses. Results are validated against x‐ray computed tomography with a typical accuracy of 0.081 mm.

Active sensing ultrasonic guided wave-based damage diagnosis via stochastic stationary time-series models

In the context of acousto-ultrasonic guided wave-based structural health monitoring, a statistical damage detection and identification (collectively referred to as damage diagnosis) framework for metallic and composite materials is proposed. Stochastic stationary time-series autoregressive (AR) models are used to model the ultrasonic wave propagation between piezoelectric actuator-sensor pairs on structural components and enable the damage diagnosis process via the use of the AR estimated parameters and corresponding covariance matrices. The proposed method exploits guided wave signals including the reflection parts, and thus the extraction of the S0 and/or A0 modes is not necessary, while the statistical properties and variation of estimated model parameters with respect to damage intersecting and non-intersecting wave propagation paths are presented and assessed. To investigate the method’s performance and robustness, two variations are proposed based on the singular value decomposition and principal component analysis. The obtained modified AR parameter vectors are then used to estimate appropriate statistical characteristic quantities used to enable the damage detection and identification tasks. The diagnosis is based on properly defined statistical hypotheses decision-making schemes and predetermined type I error probabilities. The performance and applicability of the method are explored experimentally via a series of tests on aluminum and composite coupons under various damage scenarios for damage intersecting and non-intersecting paths. The results of the present study demonstrated the effectiveness and robustness of the proposed modeling and diagnostic framework for guided wave-based damage diagnosis that can be implemented in a potentially automated way.

Enhanced fatigue life of additively manufactured high-strength TiB2-reinforced Al-Cu-Mg-Ag composite through in-process surface modification during hybrid laser processing

ABSTRACT Laser powder bed fusion (L-PBF), an additive manufacturing (AM) technique, often leads to parts with high surface roughness in as-built condition, hence limited fatigue performance. This paper showcases the favourable impact of applying an in-process surface modification, adopting a hybrid laser processing technique (dual-laser PBF (dL-PBF)), on the three-point bending fatigue life of TiB2-reinforced Al-Cu-Mg-Ag composite coupons. The dL-PBF process parameters are optimised for this high-strength aluminium-based metal matrix composite, followed by a comparative study between 3 surface conditions, i.e. as-built, dL-PBF processed, and milled, focusing on surface roughness, concomitant stress concentration factor, surface residual stress, sub-surface hardness, sub-surface microstructure, and fatigue performance. While no significant hardness or microstructural differences are found, surface roughness and stress concentration factor are substantially decreased (> 50%) and identified as the primary factors for the significantly enhanced fatigue performance of dL-PBF processed TiB2-reinforced Al-Cu-Mg-Ag composite parts with up-facing inclined surfaces.

Minimizing environmental degradation in fracture toughness of carbon fiber/epoxy composites using carbon nanotubes

Environment assisted degradation in mechanical properties is a major concern for the integrity of composites in structural applications. Experiments are performed to examine the efficacy of carbon nanotubes (CNTs) to counter the adverse effect of environmental conditions on the fracture toughness of carbon fiber/epoxy composites (CFRP). Composite coupons are exposed to accelerated weathering cycle for varying durations. Experimental testing shows that the fracture toughness degrades significantly after exposure to aging cycle. The addition of CNTs minimizes the adverse effect of weathering. The comparable fracture toughness of 1000 hrs aged CNT modified CFRPs with the unaged conventional CFRPs suggest that the advantages of CNT addition persist even after exposure to prolong weathering conditions. Fractography analysis reveals that the CNT induced toughening of epoxy improves Mode I and Mode II fracture toughness of conventional CFRPs. While the fracture in conventional CFRP is primarily at fiber/matrix interface, textured microflow, larger sized cusp and matrix cracking are observed in CNT modified CFRPs.

Bilayer coating strategy for glass fiber reinforced polymer composites toward superior fire safety and post-fire mechanical properties

The inherent heat and fire vulnerability from the polymer matrix of fiber-reinforced polymer composites (FRPs) contributes to fire propagation, matrix decomposition and especially loss of structural integrity during fire hazards. Applying surface fire protective coating is a popular approach without sacrificing mechanical properties. In this work, the influence of fire protective coating on the fire safety and post-fire mechanical properties of FRPs with an ingeniously designed coating bilayer composition. The combustion behavior study showed that the bilayer substantially postpones the decomposition of the polymer matrix through the thickness, showing a reduction of 50 % and 65 % for peak heat release rate and total smoke production respectively. Fire insulation tests showed good thermal insulation capabilities with no burn-through. Furthermore, the tensile strength of protected composite coupons was screened and showed a retention of 79 % original tensile strength after suffering 120s of heat/fire attack. This investigation resulted in a proposed protective strategy and mechanism offering a meaningful approach to enhancing the fire safety and fire structural integrity of polymer composites.

Application of the effective crack length method to model delamination of unidirectional composite laminates under Mode II shear loadings

Damage modelling of composite material delamination is an intense field of research to understand the complex composite failure behaviour and predict the residual strength of damaged structures. One of the widely employed methods to simulate delamination is the cohesive zone modelling (CZM) technique. To successfully utilize this approach, accurate characterisation of the interlaminar fracture toughness is crucial, while the composite delamination is dominated by Mode I and Mode II fracture in most cases. Numerous studies have been conducted on composite materials delamination under Mode I loadings using double cantilever beam (DCB) tests. Accordingly, the ASTM standard testing procedure and data reduction scheme to obtain Mode I fracture toughness (GIc) have been well established and widely accepted. However, it is still challenging to characterize the composite Mode II delamination resistance due to the susceptibility problems inherent to the existing testing methods and the lack of robust data reduction schemes to accurately identify the initial crack tip and monitor the crack growth. This study attempts to find a reliable solution to obtain the Mode II fracture toughness (GIIC) and an effective modelling strategy to simulate Mode II delamination in laminated composites. First, we reviewed the existing testing set-ups and surveyed the data reduction schemes conventionally used to obtain GIIC. The advantages and drawbacks of the three most used test methods, and particularly the standard end-notched flexure (ENF) test (ASTM D7905/D7905M) and the end-loaded split (ELS) test (ISO 15114:2014) were examined. Second, the advantages of the effective-crack-length-based data reduction schemes against the classical data reduction schemes were empirically studied with the ENF tests conducted on G40-800/5276-1 carbon-fibre reinforced composite laminate coupons. Although many studies have studied the accuracy of the effective-crack-length-based approaches from different aspects, there is a lack of direct comparison between the numerical results and experimental data. Our modelling study demonstrates that among the five data reduction schemes that are examined, the compliance calibration method (CCM) required by ASTM D7905 yields the most conservative GIIC values, which is suitable for establishing material property for a design purpose. The compliance-based beam method (CBBM) may generate the least conservative GIIC values, which are deemed to be the most accurate ones for modelling and simulation validation purposes. Finite element (FE) modelling of the ENF tests using the CZM technique was carried out and comprehensive parametric studies were conducted to achieve an efficient and robust strategy for delamination modelling of composite laminates under Mode II shear loadings.

Objective determination of peridynamic material parameters for fiber-reinforced composites with shear nonlinearity – Part 1: Elastic properties

An objective approach is presented for determining peridynamic (PD) material parameters for the nonlinear pre-peak behavior of fiber-reinforced composite laminates. The fiber and matrix material regions are explicitly represented. The pre-peak behavior of laminae exhibiting different degrees of nonlinearity depending on the fiber orientation is represented by the PD adaptations of the Ramberg–Osgood (RO) and hyperbolic relationships. The approach is extended to capture the nonlinear inter-laminar response for laminates. The PD method is validated against experiments for several off-axis composite coupons under quasi-static tension. The current approach accurately captures the nonlinear pre-peak material behavior of fiber-reinforced composites.