Macroscopic Stress Strain Response Research Articles

A machine learning method of accelerating multiscale analysis for spatially varying microstructures

Multiscale computing for heterogeneous materials provides a powerful and fidelity approach to handling situations where a suitable macroscopic constitutive model is unavailable. However, there have been very few instances in the industrial sector where concurrent multiscale modeling techniques have been adopted, primarily because they require significant computational resources. In particular, when dealing with large numbers of representative volume elements (RVEs) with different microstructure morphologies throughout the macrostructure. In this paper, the novelty lies in providing an artificial neural network (ANN) model-based multiscale approach for accelerating multiscale analysis of the elliptical inclusion-reinforced composites with spatially varying microstructures, which give up the assumption of global periodicity. To tackle this challenge, firstly, a series of RVEs with different microstructure morphologies characterized by inclusion orientations and aspect ratios, under different load conditions, are simulated to generate training data. Second, the back propagation neural network (BPNN) is trained offline using data acquired from the RVE simulation for learning the underlying and possibly RVE morphologies. The trained BPNN replaces the complex microscopic mechanical solution problems over each macroscopic integration point at each iteration, to update the macroscopic stress-strain responses and it significantly reduces the computational cost of multiscale simulations. Then, the trained neural network is implemented on ABAQUS via user-defined materials (UMAT) and its effectiveness is verified by comparison with the classical multiscale finite element method (FE2) method. Finally, the outstanding computational capability of the proposed approach is further demonstrated through two numerical examples.

Nanoindentation behaviour simulation of a polycrystalline NiTi shape memory alloy using the crystal plastic finite element method

Polycrystalline NiTi shape memory alloys (SMAs) are inevitably involved in plastic deformation under the action of an external force, thus significantly affecting the mechanical behaviour of materials. To deeply understand the plastic deformation mechanism of the NiTi SMA at 400 ℃, the representative volume element (RVE) model combined with the crystal plastic finite element method and the improved Voronoi algorithm were used to construct a three-dimensional polycrystalline spherical nanoindentation model for studying the contribution of different slip systems to the plastic deformation. The calculation results show that the constructed polycrystalline model can well match the experimental curve of the macroscopic stressstrain response curve of the polycrystalline NiTi SMA; the nanoindentation curve also confirms this result. Based on the constructed 3D polycrystalline nanoindentation model, three slip systems ({110}<100>, {010}<100>and {110}<111>) were introduced at the same time. According to the average cumulative shear strain calculated during the indentation process, the results show that the {110}<111> slip system provides the largest contribution to plastic deformation, and the {010}<100>slip mode provides the smallest contribution. The elastic modulus of the model was calculated using the Oliver-Pharr method, and the calculated results are consistent with the experimental results, which proves the validity of the model.

Tension-compression asymmetry of metastable austenitic stainless steel studied by in-situ high-energy X-ray diffraction

This work studies the tension-compression asymmetry (TCA) of metastable austenitic stainless steel (MASS) in uniaxial loading depending on temperature. In-situ high-energy X-ray diffraction was used to simultaneously probe phase fractions, transformation kinetics, crystallographic texture, lattice strains, strain and stress partitioning between austenite and martensites during quasi-static tensile and compressive deformation at 24, 60 and 100 °C. Complementary relaxed-constraint crystal plasticity simulations and calculations of the mechanical driving force related to the formation of α’ and ε martensites were performed. At 24 °C, martensitic transformations (MTs) prevail, while at 100 °C dislocation slip is the dominant deformation mechanism for both load senses. Macroscopic stress-strain response and transformation behaviour exhibit TCA, with compression promoting the conversion of ε into α’. Transformation kinetics were analyzed in relation to shear banding and the geometric alignment of ε lamellas depending on load sense and temperature. A strong TCA was found for crystallographic texture, bearing signatures of grain rotation due to plastic slip and of MT in case of austenite (γ). For both load senses, the relative strengths of austenite and martensite texture fibres were related to the driving force anisotropy for α’ formation calculated based on the phenomenological theory of martensite crystallography. Texture evolution of α’ is largely controlled by the MT itself, not by grain rotation. Analysis of differently orientated austenite grain families revealed a pronounced TCA of the lattice strains, linked to the γ → ε MT. This was found to be a direct consequence of driving force and volume change related to ε formation. Furthermore, stress is shared differently between austenite and martensites in tension vs. in compression. γ hardens more and hence carries a larger portion of the total stress in compression than in tension. The origin for this TCA could be found in the elasto-plastic accommodation of the volume change related to α’ formation. These findings can aid the development of new material laws for MASSs that are sensitive to load-sense and temperature for advanced forming simulations.

Evaluating the adhesion response of acrylonitrile-butadiene-styrene (ABS)/thermoplastic polyurethane (TPU) fused interface using multiscale simulation and experiments

This paper implements reactive forcefield molecular dynamics (MD) simulation to evaluate the mechanical performance of the fusion bond line formed between acrylonitrile butadiene styrene (ABS), and thermoplastic polyurethane (TPU). The simulated interfacial adhesion responses, as obtained from MD simulation, are further implemented as the interfacial properties between ABS and TPU in an upscaled cohesive zone-based finite element analysis (FEA) model for macroscopic response evaluation. Such upscaling enables fair comparison of the simulated macroscopic stress–strain response with experimental results obtained for 3D printed ABS/TPU hybrid samples with a fusion-bonded interface. Overall, the stress–strain response predicted from a FEA-based model shows a good correlation with the experimental data signifying good predictive efficacy of the simulation approach. Thus, by interactively linking the molecular structures of the polymers and the processing parameters with the macroscale interfacial adhesion response of the fusion bond line, the experimentally validated comprehensive approach presented in this paper paves the way for atomistic engineering of the molecular structures as well as efficient fine tuning of processing parameters to meet desired macro-scale performance needs besides enabling exploration of the mechanisms and atomistic origins of the interfacial damage at the fused bond line.

In situ biaxial loading and multi-scale deformation measurements of nanostructured materials at the CoSAXS beamline at MAX IV Laboratory.

Characterization of the mechanical response of polymers and composite materials relies heavily on the macroscopic stress-strain response in uniaxial tensile configurations. To provide representative information, the deformation process must be homogeneous within the gauge length, which is a condition that is rarely achieved due to stress concentration or inhomogeneities within the specimen. In this work, the development of a biaxial mechanical testing device at the CoSAXS beamline at MAX IV Laboratory is presented. The design facilitates simultaneous measurement of small- and wide-angle X-ray scattering (SAXS/WAXS), allowing assessment of the microstructural configuration before, after and during the continuous deformation process at multiple length scales. The construction also supports multiple deformation conditions, while guaranteeing stability even at high loads. Furthermore, the mechanical experiments can be complemented with spatially resolved mesoscopic surface deformation measurements using 3D-surface digital image correlation (DIC). Polycarbonate (PC) was used to demonstrate the varied material response to multi-axial deformation, as PC is isotropic with a high glass transition temperature (∼150°) and high strength. As a result, a clear correlation between full-field methods and the microstructural information determined from WAXS measurements is demonstrated. When a uniaxial load is applied, homogeneous strain regions could be observed extending perpendicular to the applied load. When a secondary axial load was added (biaxial mode), it was observed that high strain domains were created near the centre of the sample and at the boundaries after yield. With increased strain, the deformation in the main deformation direction also increases. Mechanical reliability was demonstrated by carrying out static loading of polyacrylonitrile-based carbon fibre (CF) bundles. As a result, the nonlinear stiffening behaviour typically observed in CFs was seen, while no evidence of the creation of new voids during loading was observed. The results support the reliability and broad applicability of the developed technique.

Microstructure characterization and elastic-plastic self-consistent simulation studies of anisotropic deformation of [formula omitted]-tin

Uniaxial compression tests of 99.9% pure polycrystalline β-tin (Sn) were conducted at various strain rates (10−3/s, 10−1/s and 1/s) and temperatures (294 K and 193 K) to understand the effects of these variables on the stress–strain response, microstructure evolution, and stress relaxation behavior. Multiple Sn specimens were subjected to complex compressive loading/unloading/reloading paths at different strain rates. Specimens initially compressed at higher strain rates showed strain rate-dependent texture evolution and more pronounced relaxation upon reloading, as compared to those pre-strained at lower rates at room temperature (RT). Compression tests conducted at low temperature (193 K) revealed increased strength, similar to the enhanced strength observed when the strain rate was increased at RT. Neutron diffraction was employed to characterize the initial and final bulk textures of the RT specimens. Electron backscatter diffraction was utilized to examine the crystallographic grain orientation and morphology, thereby identifying the signatures of dislocation-mediated deformation, grain refinement, recrystallization, and twinning behaviors. Elastic-plastic self-consistent simulations were performed to investigate the deformation modes responsible for the strain rate-dependent macroscopic stress–strain response and texture evolution. Effects of crystallographic orientation on stress relaxation behavior was also examined. The model predictions are in reasonable agreement with experimental observations.

Experimental investigation of microscale mechanisms during compressive loading of paperboard

Compression of paperboard is a common procedure during industrial package forming and better knowledge of the material response is needed to avoid defective packages and waste. To go beyond current modelling approaches, experimental identification of mechanisms underlying the macroscopic stress–strain responses is needed. In this study, in-situ uniaxial compression of paperboard is studied through synchrotron tomography at high spatiotemporal resolutions. Both the microstructural evolution of the fibre network and the actual boundary conditions of the loading were quantified and analysed. At the microscale, the loading equipment plates were not perfectly flat resulting in an increasing sample-equipment contact area with loading. This is, however, shown to only have a small effect on the form of the macroscopic stress–strain curves. The evolution of 3D strain fields showed that strain accumulated close to the sample surfaces in the early part of the compression process, whereafter the main deformation zone shifted to the out-of-plane centre. Both fibre walls and pore volumes were observed to decrease during loading (and recover partly after unloading). Regarding the pore volume, the main reduction mechanism was seen to be closure of layers between fibres. Even if the total pore volume reduction was seen to be the dominant deformation mechanism in a second stage of compression, the volumetric change of fibre walls was non-negligible. Fibre wall compression is not commonly considered in theoretical treatments of paperboard compression, but this work suggests that the stored elastic energy could be a driver for the elastic recovery of the fibre network during unloading.

Implementation and experimental validation of nonlocal damage in a large-strain elasto-viscoplastic FFT-based framework for predicting ductile fracture in 3D polycrystalline materials

Ductile materials, such as metal alloys, can undergo substantial deformation before failure. Additionally, these materials are usually of polycrystalline composition and exhibit strongly anisotropic behavior at small length scales. Previously developed fast Fourier transform (FFT)-based models can model ductile fracture of isotropic materials or the elastic–plastic behavior of anisotropic polycrystalline materials; however, there remains a need to couple both capabilities. This work extends a large-strain FFT-based crystal plasticity model to simulate ductile fracture of polycrystalline materials. A triaxiality-based continuum damage mechanics (CDM) formulation is incorporated into a large-strain elasto-viscoplastic FFT (LS-EVPFFT) framework. The CDM formulation is augmented with an integral-based nonlocal regularization approach that correctly handles gas-phase material necessary to model unconstrained surfaces. To validate the damage-enabled LS-EVPFFT framework, mesoscale copper tensile coupons were machined using microwire electrical discharge machining and experimentally characterized using electron backscatter diffraction. In-situ optical digital image correlation was performed during uniaxial testing to provide a side-by-side comparison of the experimental and computational strain fields and stress–strain responses. The damage-enabled LS-EVPFFT framework can simulate the complete macroscopic stress–strain response of ductile polycrystals to failure. The model reproduces necking behavior that qualitatively agrees with experimental observations. By leveraging the relatively low computational cost of the damage-enabled LS-EVPFFT framework, the framework presented here allows the ductile fracture response of 3D polycrystalline materials to be tractably predicted.

On mesoscale modeling of concrete: Role of heterogeneities on local stresses, strains, and representative volume element

The mechanics of concrete can be understood comprehensively only if its heterogeneous microstructure is considered in experiments and simulations. We combine mesoscale modeling, in-situ X-ray computed tomography imaging, and in-situ 3D X-ray diffraction measurements for one of the first times to investigate the role of heterogeneities on macroscopic and microscopic responses in concrete. The focus here is on heterogeneities at the micron scale: aggregates, cement paste, interfacial transition zone, high-density phases, and voids. We specifically seek to answer whether all levels of heterogeneities are essential in predicting: (a) elastic macroscopic stress–strain response, (b) microscopic elastic stress–strain concentrations, and (c) representative volume element size for elastic responses. The results demonstrate the significant influence of heterogeneities on local strains in matrix phases and the minimal influence of heterogenities on stresses in individual grains.

Stress shielding in laser melting multilayered nickel-base superalloys under monotonic and cyclic loadings

In the present work, the mechanical properties and fatigue performance of laser melted mismatching nickel-base superalloys were investigated by multiscale experiments and computations. It confirmed that the local strength degradation does not affect the macroscopic stress–strain responses and overall low-cycle fatigue performance due to the stress shielding in the remelting material. The stress shielding mechanism was quantitatively illuminated and the critical shielding criterion was established. Accumulation of cyclic plastic deformations stimulates the cyclic stress softening and complete tensile mean stress relaxation in the remelting material, which significantly decreases the fatigue driving force of the mismatching material.

Multiscale plasticity behavior and fatigue performance of laser melting multi-layer nickel-based superalloys upon heat treatments

The present work focuses on heat treatment effects on cyclic plasticity behavior, multiscale strengthening mechanisms and low cycle fatigue performance of laser melting nickel-based superalloys. Microscopic indentation analysis, mesoscopic DIC analysis and macroscopic material testing were conducted to identify multiscale mechanical properties. A DIC-aided indentation method was developed to identify the constitutive parameters of the laser melting material by introducing the reference material. The dendritic–cellular microstructures in the remelting zone (RZ) significantly decrease the effects of the grain size and morphology. Heat treatments can improve the strength but decrease the ductility of RZ and do not affect the macroscopic stress–strain responses of the multilayered material. Moreover, the strengthening mechanisms in the laser melting material were verified to reveal size- and plasticity-dependent effects. The strengthening contributed by grain boundaries and twin boundaries yields little effect on the strength at micro scales and the influences increase with plastic deformations. Furthermore, the aging treatment increases the fatigue life of RZ by factor 2 and, however, decreases the low cycle fatigue performance of the multilayered material, meaning that the under-matched material can be stronger than the base material in certain configurations. The stabilized fatigue load of the laser melting material has strong correlations with the mismatching and loading levels. The present study provides a deep insight into the strengthening mechanisms and cyclic plasticity behaviors of laser-manufactured materials.

Macroscopic Stress-Strain Response and Strain-Localization Behavior of Biopolymer-Treated Soil.

The enhancement of soil engineering properties with biopolymers has been shown recently as a viable and environmentally benign alternative to cement and chemical stabilization. Interest in biopolymer-treated soil is evident from the upsurge of related research activities in the last five years, most of which have been experimental in nature. However, biopolymers have not yet found their way into engineering practice. One of the reasons for this may be the absence of computational models that would allow engineers to incorporate biopolymer-treated soil into their designs. Therefore, the main goal of this study is to numerically capture a macroscopic stress-strain response and investigate the effect of biopolymers on the onset of strain localization. Several diagnostic strain-localization analyses were conducted, thus providing strain and stress levels at the onset of strain localization, along with the orientations of the deformation band. Several unconfined compression and triaxial tests on the plain and biopolymer-treated soils were modeled. Results showed that biopolymers significantly improved the mechanical behavior of the soil and affected the onset of strain localization. The numerical results were confirmed by the digital image analysis of the unconfined compression tests. Digital image processing successfully captured high strain concentrations, which tended to occur close to the peak stress.

Synchronous involvement of topology and microstructure to design additively manufactured lattice structures

This article presents a methodical approach to optimize microstructure (e.g., the crystallographic texture) and topology (e.g., unit cell and struts) concurrently to improve the mechanical properties of additively manufactured metallic lattice structures (AMLS), i.e., yield strength and plastic flow stress. Full-field elasto-viscoplastic Fast Fourier Transform (EVP-FFT) crystal plasticity (CP) simulations are employed to determine the optimal microstructure. The CP model parameters were calibrated to measured macroscopic stress–strain response and microstructural data for polycrystalline samples of additively manufactured (AM) Inconel 718 with solution treated and aged (STA) microstructure. Since the crystallographic orientation of the constituent single-crystal grains with respect to the loading direction has a significant impact on the mechanical behavior of the material, stress projection factor analysis was used to determine four candidate textures to explore in for a given unit cell topology. Full-field crystal plasticity simulations were used to determine macroscale yield surface parameters for each of the considered textures, thereby enabling macroscale lattice unit cell simulations that account for the underlying microstructure. The calibrated microstructure-dependent yield surfaces are used to investigate the effect of different microstructures on the mechanical response of different LS topologies with the same relative density. The results show that in a texture with <111> crystallographic direction, parallel to the loading direction, the tensile and compressive yield strength are 20% and 58% larger, respectively compared to the AM STA IN718 texture. Furthermore, when this texture is used in conjunction with the Rhoctan topology, the results demonstrate 50% improvement in both the yield strength and modulus of elasticity relative to previously optimized AMLS designs that did not directly account for microstructure. This simultaneous consideration of microstructure and topology during optimization, thus, significantly enhances the structural integrity of the AMLS.

Deformation behavior of CP-titanium under strain path changes: Experiment and crystal plasticity modeling

The deformation behavior of commercially pure rolled titanium subjected to strain path changes is studied using experiments and a crystal plasticity model. Four different loading combinations are performed at room temperature to study the activation of slip, twinning, de-twinning and double-twinning in hexagonal closed packed titanium. The strain paths considered are: rolling direction compression (RDC) followed by normal direction compression (NDC), RDC followed by transverse direction compression (TDC), NDC followed by RDC, and NDC followed by TDC. An EBSD-based analysis of the distribution of boundary misorientation angles before and after reload was developed to analyze the evolution of {101¯2} tensile and {112¯2} compression twins. This analysis supports the model results concerning the treatment of twin reorientation. A de-twinning and double-twinning model accounting for back stress effects, an important feature of strain path changes, is implemented within the framework of the visco-plastic self-consistent (VPSC) model along with a dislocation density (DD) based hardening scheme. In the model, plasticity is accommodated by prismatic 〈a〉, basal 〈a〉 and pyramidal 〈c+a〉 slip modes, and {101¯2} tensile and {112¯2} compression twinning modes. The VPSC model predicts the evolution of twinning, de-twinning and double-twinning processes for both tensile and compression twinning modes under strain path change. The model predicts macroscopic stress-strain response, texture evolution, and twin volume fraction that are in agreement with experimental observations. The evolution of texture is investigated in detail by separately analyzing the twinned domains, rather than the evolution of the global texture.

Multi-scale modelling of progressive damage and failure behaviour of 2D woven SiC/SiC composites

In this paper, a multi-scale modelling approach has been developed to predict the progressive damage and failure behaviour of 2D woven SiC/SiC composites. At the tow scale, non-linear tow properties have been determined by a micromechanics-based damage model, in which two scalar damage variables were introduced to characterize the fibre-dominated and matrix-dominated damage, respectively. Based on periodic boundary conditions, a meso-scale unit cell model has been established to simulate the macroscopic stress-strain responses and progressive damage processes of the composite under uniaxial tensile, compressive and in-plane shear loadings, respectively. In the numerical method, the non-linear properties of constituent materials have been implemented by the user defined subroutine, USDFLD of the finite element package, Abaqus. The numerical results and their comparisons with experimental stress-strain curves have been presented. The failure mechanisms of the composite under each loading have been also discussed. The high efficiency and prediction accuracy of the model make it possible to analyse large scale woven composites.

Spurious softening in the macroscopic response predicted by the additive tangent Mori–Tanaka scheme for elastic–viscoplastic composites

The Mori–Tanaka (MT) scheme is a well-established mean-field model that combines simplicity and good predictive capabilities. The additive tangent MT scheme is a popular variant of the method that is suitable for elastic–viscoplastic composites. This work is concerned with the analysis of some intrinsic features of the additive tangent MT scheme, in particular, of spurious softening in the macroscopic response that may be encountered when the Perzyna-type viscoplasticity model is used. The resulting non-monotonic macroscopic stress–strain response is clearly non-physical, but it also has a negative impact on the efficiency and robustness of the MT model when it is used as a local constitutive model in concurrent multiscale finite-element computations. As shown in the paper, the spurious softening is more pronounced when the so-called soft isotropization is employed to compute the viscoplastic Hill tensor, but it is also observed, although for a much narrower range of material parameters, in the case of the hard isotropization and when no isotropization is applied. Moreover, the softening is promoted at low strain rates, for high elastic contrast, and for high volume fractions of inclusions. Nevertheless, if the soft isotropization is avoided, the additive tangent MT scheme proves to be a feasible and computationally robust mean-field model that can be successfully employed in finite-element computations.

Tuning critical resolved shear stress ratios for bcc-titanium Ti21S via an automated data analysis approach

We introduce a novel method for automated slip trace detection and analysis based on the Hough transform algorithm and apply it to electron channeling contrast imaging micrographs. This is further augmented with an automation procedure for the determination of slip-trace crystallography in conjunction with orientation data acquired via electron backscattered diffraction. Automation is required for faster indexation of the slip traces and for more reliable statistical studies. The automation procedure was applied to different regions of interest on a β-Ti21S sample loaded in situ in tension. β-Ti21S is a bcc alloy with 48 slip systems available to accommodate plastic deformation, including all complexities associated with pencil glide. Multiple regions of interest were analyzed using the automation procedure. The acquired slip distribution statistics reveals that the majority of the slip traces belong to the {112} and {123} slip families. The deformation response of the observed regions of interest was also simulated using a full-field crystal plasticity model implemented in DAMASK, based on a phenomenological power law based constitutive formulation, incorporating all potentially active 48 slip systems. The slip system activity distribution from modelling is compared with the slip distribution statistics observed experimentally. The plasticity parameters for β-Ti21S were taken from the literature and the critically resolved shear stress (CRSS) values were adjusted to match the experimentally observed yield stress value. We begin with uniform CRSS ratios for all three potential slip system families and tune the CRSS ratios to match the slip-distribution statistics experimentally, keeping the average CRSS value the same for all cases. Thus, a method has been introduced to tune average CRSS values and ratios by considering both the macroscopic stress–strain response and the locally observed slip-distribution statistics, obtained via automated slip trace detection procedure.

Lattice strain development in an alpha titanium alloy studied using synchrotron and neutron diffraction

Neutron and high-energy X-ray diffraction methods have been used to investigate deformation mechanisms (slip and twinning activities) during uniaxial tensile tests of Grade 1 commercially pure titanium (Ti-α). These two diffraction techniques have provided valuable and complementary information. The predictions made by an Elasto-Plastic Self-Consistent (EPSC) model, taking into account grain reorientation and stress relaxation induced by twinning activity, have been compared with the experimental data. Results clearly demonstrate that there is a good agreement between simulations and diffraction measurements. The EPSC model enables accurate predictions of: (i) the lattice strains developed in variously oriented {hk.l} grain families within the bulk material, (ii) the grain reorientation induced by twinning activity and (iii) the macroscopic stress-strain response. Two different textured products were studied in order to evaluate the influence of texture on the mesoscopic and macroscopic responses of Ti-α alloy.

Anisotropy evolution of elastomeric foams during uniaxial compression measured via in-situ X-ray computed tomography

We have characterized the three-dimensional evolution of microstructural anisotropy of a family of elastomeric foams during uniaxial compression via in-situ X-ray computed tomography. Flexible polyurethane foam specimens with densities of 136, 160 and 240 kg/m3 were compressed in uniaxial stress tests both parallel and perpendicular to the foam rise direction, to engineering strains exceeding 70%. The uncompressed microstructures show slightly elongated ellipsoidal pores, with elongation aligned parallel to the foam rise direction. The evolution of this microstructural anisotropy during deformation is quantified based on the autocorrelation of the image intensity, and verified via the mean intercept length as well as the shape of individual pores. Trends are consistent across all three methods. In the rise direction, the material remains transversely anisotropic throughout compression. Anisotropy initially decreases with compression, reaches a minimum, then increases up to large strains, followed by a small decrease in anisotropy at the largest strains as pores collapse. Compression perpendicular to the foam rise direction induces secondary anisotropy with respect to the compression axis, in addition to primary anisotropy associated with the foam rise direction. In contrast to compression in the rise direction, primary anisotropy initially increases with compression, and shows a slight decrease at large strains. These surprising non-monotonic trends and qualitative differences in rise and transverse loading are explained based on the compression of initially ellipsoidal pores. Microstructural anisotropy trends reflect macroscopic stress-strain and lateral strain response. These findings provide novel quantitative connections between three-dimensional microstructure and anisotropy in moderate density polymer foams up to large deformation, with important implications for understanding complex three-dimensional states of deformation.

Experimental and numerical investigation of progressive damage and failure behavior for 2.5D woven alumina fiber/silica matrix composites under a complex in-plane stress state

The focus of this work is to characterize the progressive damage and failure behavior of 2.5D woven alumina fiber reinforced silica ceramic matrix thin composite specimen under a planar tension-shear stress state. The tensile and shear stress–strain diagrams in the principal material coordinate system were obtained using the off-axis tension test with the digital image correlation technique. A mesoscale finite element model of the composite material was developed within the framework of continuum damage mechanics. The thickness effect on the macroscopic mechanical response was considered by removing the periodic boundary conditions along the thickness direction. The macroscopic stress–strain response given by the numerical model was validated by the experimental results. The interaction of the planar biaxial tension and shear stresses was taken into account in the model, quantified using a shear contribution coefficient in the modified 3D Hashin failure criterion. The results from the damage evolution analysis indicate that the linear tensile stress–strain response with a brittle fracture characteristic for the on-axis tension specimen is governed by the axial fiber bundle. The nonlinear tensile stress–strain response with the significantly reduced ultimate stress under biaxial tension and shear stress state results from multiple damages with evolution in both axial and transverse fiber bundles. Both the effective tensile modulus and the ultimate tensile strength increase with increasing the thickness of the specimen due to the increase of the fiber volume fraction. The strengthening induced by the size effect is less significant for the specimen under biaxial tension and shear stress state than that for the on-axis tension specimen owing to the involvement of shear response dominated by the matrix of the material. The results of this study provide new insight into the failure of 2.5D woven ceramic-based composite material, which contributes to the optimal design of the reusable thermal protection system structure.