Hydrothermal aging of the polymer matrix can significantly impact the long-term performance of short fiber reinforced thermoplastic composites (SFRTs), yet the extent of this influence remains unclear due to complex contributing factors. In this study, thermostatic immersion aging followed by tensile test is performed for polyamide (PA) and its composites reinforced with short carbon fiber and glass fiber, with variations in fiber content, geometric characteristics, and aging temperature. Despite differing diffusion rates and saturation levels among materials, all systems follow Fickian diffusion kinetics. To model the modulus degradation due to aging, a two-step homogenization (TSH) framework is developed by sequentially applying the Bridging Model and a hybrid method. The aged modulus is estimated by replacing the pristine matrix modulus with its moisture-degraded counterpart. However, predicting strength is more challenging due to the complex interplay between matrix plasticization and pore growth, as revealed by comparative CT imaging and tensile test results. Therefore, a Random Forest regression model is trained using 181 data points to predict the elastic modulus, tensile strength, and failure strain of SFRTs based on six input features. All predictions achieved R2 values above 0.96 on the testing dataset, confirming the adequacy of the selected input features. Regarding feature importance, SHAP analysis identifies fiber volume fraction, moisture content, and fiber-to-matrix modulus ratio as the most influential variables. The minimal effect of aging temperature further supports the TSH assumption that moisture-driven changes in the matrix govern the mechanical degradation behavior of SFRTs in this system.

Compression behaviors of single-stiffener composite panels with and without initial debonding between the skin and stiffener are investigated in this paper. The coupling mechanisms between a buckling deformation and damage evolution, particularly skin-stiffener debonding, are considered. At the skin-stiffener interface, the Cohesion free method (CFM) is employed to assess debonding initiation and growth by inserting secondary-layers, whose stress fields are modified by mesh-dependent modification coefficients (MCs), at the potential fracture interfaces. Within the skin and stiffener, intralaminar failures including fiber breakage, matrix crack and fiber-matrix interface debonding are analyzed through micromechanics Bridging Model. The compression-induced collapse of a stiffened composite panel can be captured when a fatal failure is attained. All of the experiments for the material inputs can be carried out independently, following existing standards. By means of post-buckling analysis based on the first eigenmode of the stiffened panel, the deformation, skin-stiffener debonding and intralaminar failures within each lamina are visually presented. The predicted buckling shapes, skin-stiffener debonding areas and fatal failure loads of all the four panel configurations under consideration agree well with the available experimental counterparts and exhibit consistency across varying mesh sizes, demonstrating the effectiveness of the proposed stress analysis and failure identification methods. The overall computational time is reduced by more than 30% compared with that using the traditional fracture tracking models.

A calibration-free method called Cohesion Free Method (CFM) for predicting interlaminar fractures of any bi-material has been established recently by this author. Only two peak data from the double cantilever beam (DCB) and end-notched flexure (ENF) tests relevant to the bi-material interface are required, which are used to determine two stress modification coefficients (MCs), in addition to the basic property parameters of the materials involved. As analytical formulae to evaluate the stress fields of the DCB and ENF samples inserted with a pure matrix layer along the interfaces of their initial cracks are not yet available, a finite element approach (FEA) to obtain the MCs is necessary. In this paper, an ABAQUS plugin named AutoMC is developed to implement the FEA so that any pairs of the MCs in application of CFM to the target bi-material can be automatically matched. The inputs for the AutoMC can be either the peak loads, or the peak displacements or the interlaminar fracture toughnesses. Applications of the CFM incorporated with the AutoMC to predictions of various interlaminar fractures including laminate delamination, adhesive joint crack and interface debonding between metal sheet and composite lamina have been made. Good agreements between the predictions and the available measurements demonstrate the efficiency of this work.

The accumulation mechanisms and spatial distribution of debonding damage in fiber-reinforced polymer composites under combined tension and shear loading are not well understood. To tackle this research gap, X-ray computed tomography has been utilized to observe the debonding damage between epoxy and CFPR rods in cruciform specimens. An in-situ loading rig was used to perform tension tests, with different combined stresses applied by varying the orientation of the embedded reinforcements. After loading, the damage volumes have been extracted and visualized in 3D to comprehensively examine the spatial distribution of debonding. The in-situ and ex-situ experimental results confirm that the distribution and propagation of interface cracks are largely dependent on the ratio of tension to shear and the position of adjacent reinforcements. Additionally, critical parameters such as debonding angles, crack opening displacements, and deflecting angles have been quantitatively analyzed. Based on the results, the authors proposed three representative models to describe the dimensional properties of interface cracks, and an empirical formula that reveals the positional correlation between interface cracks on adjacent reinforcements. Considering the universality of combined loading in engineering applications, a full understanding of the resulting debonding damage can significantly contribute to the optimization of composite design methodologies.

The variation in the dimensions of interface cracks during loading provides key information for the establishment of a micro-mechanical model for composites. Nevertheless, existing microscopic observations are limited, particularly concerning the multi-perspective examinations of interface debonding resulting from combined loading. To address this issue, off-axis tension was applied, and the reflected-light method and CT scanning were employed separately to investigate the propagation of interface cracks along the fiber axis direction and circumferential direction. The experimental findings suggested that the extension velocity of the interface crack in the longitudinal section remains substantially stable under transverse tension and gradually decreases under loading incorporating shear stress components. Additionally, the interface crack propagation on a transverse section includes a rapid propagation stage, a deceleration stage, and a stabilization stage. Moreover, a finite element analysis of interface debonding was developed using the ABAQUS/Standard platform. It was found that an increase in the proportion of the shear component may enhance the challenge of acquiring accurate data from both observations and simulations. Most crucially, the characteristics and formation mechanisms of unique ear-shaped interface cracks and re-closed regions were examined based on the observations and the calculated stress contour maps. In conclusion, this paper offers multi-perspective observations on the interface crack propagation under various combined loading conditions.

Epoxy resin is commonly used as the matrix in carbon fiber-reinforced polymer (CFRP), fabricated through the curing reaction of the base resin and curing agent, whose properties have a deep relationship with the crosslinking degree of the polymer. However, under certain circumstances, the desired conversion rate cannot be achieved in the experiments. To shed light on this phenomenon and the underlying mechanisms, the curing process of diglycidyl ether of bisphenol A (DGEBA) with different chain lengths and 4,4′-diamino diphenyl sulfone (4,4′-DDS) was simulated as per our previously developed crosslinking algorithm. The longer chain length postpones but does not change the reaction progress (like the gel point), leading to a lower conversion rate, and ultimately a decrease in the diffusion coefficient. In addition, the influence on the glass transition temperature is the result of the competing effects of the conversion rate and monomer diffusivity. Moreover, the negligible effect on thermal conductivity is closely linked with a slight change in the monomeric degree index (MDI), reflecting the whole internal intrinsic structure. Furthermore, the effect on Young's modulus and yield stress has a deep relationship with the ring degree index (RDI), i.e., higher RDI demands more non-bonded energy for the collective movement of monomer chains. Our systematic investigation unifies the mechanism of the impact of chain length on various thermomechanical properties, which is instructive for the improved performance of epoxy resins.

This work deals with the fiber ends debonding-induced elastic moduli degradation of a short fiber reinforced composite (SFRC). The strain fields of the matrix in a representative volume element (RVE) of the SFRC are determined from an imaginary fiber technique. By using the debonding boundary conditions, the debonded modulus of the composite is derived, which is affected by not only the far-field but also the transient solutions for the longitudinal strain of the matrix. Particularly, the imaginary fiber technique provides unbounded solution for a moderately large fiber aspect ratio. This is resolved by separating the RVE along the fiber direction into two domains. Combining the longitudinal strains in both domains, the longitudinal modulus is determined, and the longitudinal bridging tensor element in the micromechanics Bridging Model is amended. Five elastic moduli of an SFRC after the fiber end debonding are obtained on the amended Bridging Model. The effects of the fiber volume fraction, fiber aspect ratio, and fiber-to-matrix modulus ratio on the end-debonded longitudinal modulus, transverse modulus, and longitudinal Poisson's ratio are investigated.

Strength prediction of a particle reinforced polymer composite (PRPC) is still challenging. Although a PRPC is overall isotropic, it is more difficult to predict its tensile strength accurately than a continuous fiber reinforced composite (CFRC). One reason for this difficulty is that the calculation of stress fields of the constituents in a PRPC are complicated. The other reason is that the strength of a PRPC is significantly affected by interfacial strength, which is hard to be measured directly. In our research, the discount of the composite strength after debonding is attributed to the intensifying stress concentration. Two stress concentration factors (SCFs) are derived respectively to characterize the stress fluctuations in the matrix caused by the embedded particle before and after debonding. Based on the micromechanics Bridging Model and the matrix true stress theory, these two SCFs can be applied to evaluate the interface strength and the ultimate tensile strength of the composite from the properties of its component materials. Illustrations are presented to verify the efficiency of our theory and analyze the main influencing factors on the strength of the PRPC, including mechanical properties of component materials, particle size and volume fraction

Failure prediction of open-hole laminates under compression still remains a great challenge. A number of unique mechanics theories for composites developed by the author are successfully applied to analyze in plane compression induced various failures of the notched laminates in this paper. A buckling mode must be incorporated into the analysis of the compression induced delamination, and the rules for selecting a scale factor for the buckling analysis through ABAQUS are established. To simulate delamination, the interlaminar matrix stress modification method is applied. A more pertinent criterion for delamination is proposed. When and where is delamination initiated, how can the initiated delamination be propagated and how much is the delaminated area to be attained can be easily reproduced. Intralaminar failures are estimated based on Bridging Model and the matrix true stress theory. The ultimate strength of a notched laminate is assumed when any primary layer element outside neighborhoods of the stress singularity and weak singularity points firstly attains an ultimate failure. A limited, if not the minimum, number of inputs are required all measurable independently and following existing standards with no data calibration. Except for the pre-buckling analysis, no iteration is needed for prediction of all the other failures. The predicted failure modes and ultimate compressive loads of several laminates with single or double holes agree well with our measured counterparts.

One of the remaining challenges for advancing the theoretical mechanics of composite materials is to describe the relationship between interfacial debonding and the mechanical properties of composites. The fiber/matrix interfacial debonding of model composites caused by combined loading has been observed by in-situ X-ray radiography and post-mortem X-ray computed tomography (CT) in this paper. Off-axis tension (fiber axis lying at 30°, 45°, 60° or 90° with respect to the loading direction) tests have been performed on carbon fiber reinforced polymer (CFRP) cruciform specimens using an in-situ loading rig. The morphological characteristics of the cracks at the interface and in the matrix are recorded. Based on our observations, the difference between interfacial debonding caused by normal tension and tangential shear stresses and their cooperative actions in composites under combined loading have been studied. This research can give insights into interfacial debonding in composites and help to build an accurate micro-mechanical model.

Various failures of laminates under low-velocity impacts without penetration are simulated systematically with a limited number of inputs, all measurable following existing standards without any data calibration. No iteration is required to determine any of the failures investigated in this work. Any two adjacent lamina (primary) layers are inserted with a matrix (secondary) layer, whose stresses are modified through two modification coefficients (MCs). The MCs are determined through peak loads of double cantilever beam and end-notched flexure tests on unidirectional laminates, and their weak sensitivity to sample dimensions is shown. Delamination is reproduced by deleting failed secondary-layer elements. The homogenized stresses of fiber and matrix obtained by Bridging Model are converted into true values through the author’s true stress theory to estimate constituent-induced intralaminar failures, such as fiber breakage, matrix crack and interface debonding, against the monolithic fiber or matrix strengths measured independently. Primary- layer elements attaining a fatal failure (fiber breakage or matrix crack accompanied with a critical strain condition) are deleted before an impact termination corresponding to separation of the impactor from target. The predicted delamination areas and impact force, displacement and energy histories for the laminates of three lamination angles under different impact energies agree well with our measured counterparts, validating the efficiency of the simulation.

Whereas mechanics theories for isotropic materials have been almost matured, those for anisotropic or composite materials well established are only limited to linear elasticity. All of the other mechanical properties of a composite outside linear elastic range are overall lack of efficient methods to deal with. Specifically, prediction of various composite failures still remains one of the biggest challenges in solid mechanics. A fundamental reason is in that only homogenized stresses are definable and obtainable for the composite by the existing theories, and the resulting stresses in its constituent fiber and matrix materials are homogenized values as well. The mechanical properties of the composite must be estimated on a true stress level. The composite true stress theory has been systematically established by this author. Besides, a number of other analytical theories have been established by the author as well. They include the unified elastic-inelastic constitutive and internal stress evaluation theory for a composite reinforced with any continuous fibers, short fibers or particles, the incremental constitutive model for a hyperelastic material, the interlaminar matrix stress modification method for prediction of interlaminar fracture or delamination in any laminated structure, and the physics based failure criteria to detect matrix dominated composite failures. Using these theories and incorporated with a finite element approach, essentially any failure and ultimate strength of a composite structure subjected to an arbitrary static, dynamic or fatigue load can be efficiently predicted with no iteration and with a minimum number of input data all of which can be measured independently and following existing standards, as long as the void content of the composite structure can be neglected. A summary on the establishment of these theories, a complete list of the explicit formulae for them, and their applications to resolve a number of challenging problems in composite failures is presented in this paper. An Excel-table based program for achieving all the true stresses conversions is attached as a supplement. Future trends in further development on mechanics of composites are highlighted. [GRAPHICS] .

Accurately predicting ultimate strength of composite laminate is still a great challenge, especially only based on the constituent properties. In this paper, the micromechanics Bridging Model and systematic failure criteria for the constituent materials with emphasis on matrix failures subjected to three dimensional (3D) loads are compiled into a UMAT subroutine for ABAQUS to analyze failures of a laminated composite structure. The main purpose of this research is to greatly reduce calculation costs for loading conditions of in-plane tension or compression by introducing a simplified 3D finite element model based on the Pipes-Pagano theory. In all calculation cases, only the constituent properties together with the transverse tensile strength of unidirectional composite are needed as input data. Later in this paper, sufficient illustrations of 81 different composite laminates composed of 14 material systems are analyzed to confirm the practicability of this model.

The microstructure of a short fiber reinforced composite (SFRC) is different from point to point, particularly for an injection molded SFRC. In general, micromechanical models decompose such an SFRC into a set of groups, each of which contains short fibers with identical shape and orientation. We begin with examining the predictive ability of typical models, i.e., modified rule of mixture, Mori–Tanaka method, Bridging Model and Fu–Lauke scheme, for each group. Next, the effective properties of the decomposed SFRC are predicted by assembling all the groups via two-step homogenization and laminate analogous approach, respectively. The predictions are compared with FE results on representative volume elements which are constructed through a random sequential algorithm. Finally, an overall probability function that associates an LDF (length distribution function) and an ODF (orientation distribution function) with the fiber volume fraction is presented. The predictive accuracy of above decomposition methods incorporated with this function is improved.

Significant variation can be found in measurements for the longitudinal tensile strength of the same unidirectional (UD) composite. A splitting failure is one of the main reasons. It is shown in this paper that the shear stress component resulted from a longitudinal tension and a fiber misalignment can cause the matrix to fail before fiber break. The misalignment angle consists of an initial off-axial angle and a further fiber rotation during the loading. Based on the micromechanics Bridging Model and the matrix true stress theory established by the author, splitting failure has been analyzed and predicted rigorously in this paper, only using the fiber and matrix properties together with the fiber misalignment angle. The fiber initial misalignment angle of a unidirectional plate can be obtained from testing statistics, or deducing from measured longitudinal compression strength. Our research indicates that the longitudinal tensile strength and the relevant failure mode can be significantly affected by the fiber initial misalignment.

Whereas mechanics theories for isotropic materials are almost matured, only linear elastic theories for composites were essentially established. This is because only homogenized or approximated stresses are obtainable for a composite. Its mechanical properties must be estimated on a true stress level. According to Eshelby, the true stresses of the fiber are the same as its homogenized counterparts. The true stress theory for the matrix was systematically established by the author, and is reviewed and summarized in the paper. An Excel table-based program for calculating all of the possible true stress components is provided as a supplement for the reader to download. As most composite failures are caused by matrix failures, the true stress theory plays a predominant role in estimating the composite properties outside a linear elastic range. Some challenging composite failures were resolved upon the matrix true stresses, and are highlighted in the paper.

Prediction of laminate delamination can be achieved by assessing strength failure of an interlaminar matrix-layer inserted in between the laminae, but the thus obtained matrix-layer stresses are generally out of expectation. In this paper, two MCs (modification coefficients) determined from the loads for measuring Modes I and II interlaminar fracture toughnesses are utilized to refresh the normal and shear stresses of matrix-layer, so that the matrix-layer would fail before a laminate failure. This method proves appropriate to simulate delamination induced by different loads. Once the modified stresses of a matrix-layer element fulfill a strength failure condition, it is deleted and the two adjacent lamina elements are delaminated from each other. The delamination behavior and its influence on the ultimate load sustainability of the laminate are investigated. Good correlation between predicted and measured results under different loading modes confirms the efficiency of this work.

To simulate delamination in a laminate, a pure matrix secondary layer is inserted between its primary lamina layers. The stresses in the weakest secondary layer element obtained from a finite element (FE) approach must be modified since singularity or weak singularity exists at delamination point. The failed secondary layer element is deleted and delamination initiation or propagation is attained. We find in this paper that the modification coefficients before the delamination initiation can be determined by experimental data of a Short Beam Shear (SBS), whereas those after the initiation are obtained based on parameters of Double Cantilever Beam (DCB) and End Notched Flexure (ENF) tests on the unidirectional laminate. The ultimate strength of a notched laminate is assumed when any primary layer element outside neighborhoods of singularity and weak singularity attains an ultimate failure. It is shown that the neighborhood range for the weak singularity is 4 times of the primary layer thickness, while that for the singularity is 6 times of the former. No iteration is needed and all input data can be measured independently and following existing standards. Tensile strengths of four notched laminates with different lamination angles and hole diameters are studied. The simulation results agree well with the measured counterparts.

Prediction of delamination in a hybrid laminate made of steel sheet and carbon fiber reinforced plastic (CFRP) plate has been simply achieved by modifying the stresses of an interlaminar matrix layer in between the sheet and the plate. The normal and shear stresses of the matrix layer are modified with two coefficients K-h(n) and K-h(s), which are determined by the critical displacements corresponding to the peak loads applied to the double cantilever beam (DCB) and end-notched flexure (ENF) tests on the hybrid laminate. Once the modified stresses of a matrix layer element attain a tensile or shear failure, it is deleted from an incremental finite element solution process, and delamination of the laminate in between the matrix layer is considered to occur. The whole load-deflection curves of the DCB and ENF tests, and the spring back induced delamination of the steel sheet in the hybrid laminate after a U-shape drawing have been simulated. All of the pre-dicted results using the independent input data without any adjustment agree well with the measured counterparts, indicating that the stress modification method on interlaminar matrix layers is efficient for predicting delamination of a hybrid laminate. The method can be applicable to the analysis of any interlaminar fracture or delamination of an arbitrary laminated structure, as long as the laminate is adhered from individual layers using the matrix or thin adhesive films.

细观力学理论得到的复合材料内应力是均值应力,在进行破坏和强度预报前,必须转化到真实值.对于短纤维复合材料,除了轴向压缩真实应力外,基体其它方向真实应力计算已得到解决,等于其均值应力乘以基体应力集中系数.论文基于弹性力学方法得到了短纤维复合材料轴向压缩下基体的应力场,并据此定义基体的轴向压缩应力集中系数.与基体其它方向应力集中系数的定义不同,确定轴向应力集中系数时须将代表性单元分割成三部分,即一个中间部分和两个末端部分,进而获得对任意纤维长径比都适用的基体轴向压缩应力集中系数.纤维和基体的均值应力则由桥联模型解析公式计算.只需提供组分材料的几何和力学性能参数,任意长径比短纤维复合材料的压缩强度皆可方便预测.结果发现,纤维长径比和纤维含量对压缩强度都有较大影响.预报结果与实验值吻合合理,证实了论文所建理论的有效性.