Multiple Matrix Cracking Research Articles

Shear strength determining mechanism of a +/−45 laminate under tensile loading

The shear strength of a composite material is determined as a result of a complex damage and failure process, but the detailed progression has not been clearly elucidated. Here, the mechanism of determining the strength of a ±45 laminate under tensile loading is revealed from exquisitely designed experiments in conjunction with high-fidelity numerical simulation. Synchrotron radiation computed tomography is employed for extremely high-resolution images of damage status inside the composite just before its catastrophic failure. The ex situ observations discover the unique and consistent failure progression; one major matrix crack is initiated either in the +45 or −45 layer and delamination follows after the initial crack completely grows along both the fiber and transverse directions. After the delamination failure is triggered, remaining intact layers start to fail with multiple transverse matrix cracks. The failure of the intact layers is represented as a load drop in the global stress–strain curve. This sequential and interactive failure progression determines the shear strength of the ±45 laminate. The numerical analysis finds that the location of the initial matrix crack is dependent on the microstructure. Once the matrix crack is initiated, the numerical simulation exactly reproduces the experimentally observed failure process.

A progressive damage model for ceramic matrix mini-composites with thick interphases

Toughness enhancement in ceramic matrix composites (CMCs) with brittle matrix and fiber phases is often accomplished by introducing a weak finite-thickness interphase between the fiber and matrix. The current work presents a progressive damage model to predict the tensile response of single tow CMCs (mini-composite) representative of a unidirectional composite at the microscale. Implementation of a 3-phase shear-lag model for a geometrically accurate representation of the underlying microstructure in CMCs with finite thickness interphase has been highlighted. A probabilistic progressive modeling approach has been adopted, accounting for multiple matrix cracking, interfacial debonding, and fiber failure in 3-phase mini-composites. The predicted tensile response of CMCs from the progressive damage modeling approach agrees with experimental results obtained for C/BN/SiC mini-composites validating the approach.

Microstructure and tensile behavior of (BN/SiC)n coated SiC fibers and SiC/SiC minicomposites

Interphase plays an important role in the mechanical behavior of SiC/SiC ceramic-matrix composites (CMCs). In this paper, the microstructure and tensile behavior of multilayered (BN/SiC)n coated SiC fiber and SiC/SiC minicomposites were investigated. The surface roughness of the original SiC fiber and SiC fiber deposited with multilayered (BN/SiC), (BN/SiC)2, and (BN/SiC)4 (BN/SiC)8 interphase was analyzed through the scanning electronic microscope (SEM) and atomic force microscope (AFM) and X-ray diffraction (XRD) analysis. Monotonic tensile experiments were conducted for original SiC fiber, SiC fiber with different multilayered (BN/SiC)n interfaces, and SiC/SiC minicomposites. Considering multiple damage mechanisms, e.g., matrix cracking, interface debonding, and fibers failure, a damage-based micromechanical constitutive model was developed to predict the tensile stress-strain response curves. Multiple damage parameters (e.g., matrix cracking stress, saturation matrix crack stress, tensile strength and failure strain, and composite’s tangent modulus) were used to characterize the tensile damage behavior in SiC/SiC minicomposites. Effects of multilayered interphase on the interface shear stress, fiber characteristic strength, tensile damage and fracture behavior, and strength distribution in SiC/SiC minicomposites were analyzed. The deposited multilayered (BN/SiC)n interphase protected the SiC fiber and increased the interface shear stress, fiber characteristic strength, leading to the higher matrix cracking stress, saturation matrix cracking stress, tensile strength and fracture strain.

Two-scale Modeling of Composites damage with Voronoi cell finite element method for microscale computation

This paper develops an adaptive two-level computational model that includes macro and microscope analysis. Traditional displacement based finite element is used for macroscopic analysis, while Voronoi cell finite element model is used for computations of arbitrary heterogeneous domains. For an adaptive analysis, when local area may be destructive, VCFEM mesh is used instead of corresponding finite element for damage analysis. Because VCFEM model and finite element are all taken the nodal displacements as field variables, therefore, based on the idea of multigrid by the adaptive mesh adjustment, let finite element edge length and VCFEM edge length are basically the same, two kinds of elements were connected together through the use of shared nodes and use the order of the edge displacement interpolation. This formed a two-scale model of the coexistence of macro structure and micro structure. For microscale analysis, three Voronoi cell finite models (VCFEM) are build including perfect interface bonding model, interface debonding model and multiple matrix cracks model. Numerical example is executed for validating the effectiveness of the two-scale model method.

An approach to estimate crack opening displacement in two-dimensional plain-woven silicon carbide fiber-reinforced silicon carbide composite considering different matrix cracking modes

Understanding of cracking opening behavior is important for the prediction of residual strength and lifetime of silicon carbide fiber-reinforced silicon carbide ceramic–matrix composites at elevated temperatures. Under tensile loading below the proportional limit stress, multiple matrix cracking modes in the longitudinal and transverse yarns of a two-dimensional plain-woven silicon carbide fiber-reinforced silicon carbide composite appear in the matrix with debonding at the fiber/matrix interface. Crack opening displacement is a key parameter to characterize the crack opening behavior in silicon carbide fiber-reinforced silicon carbide composites and is affected by the multiple matrix cracking modes. In this article, a damage-based micromechanical crack opening displacement model for two-dimensional plain-woven silicon carbide fiber-reinforced silicon carbide composites is developed considering different matrix cracking modes. Two typical matrix cracking modes in a two-dimensional plain-woven silicon carbide fiber-reinforced silicon carbide composite, that is, cracking mode III with cracking in the matrix of the longitudinal and transverse yarns and cracking mode V with cracking only in the matrix of the longitudinal yarns, are considered. Micro stress field in the fiber, matrix of the longitudinal yarns, and transverse yarns are obtained. The crack opening displacement and related damage parameters are determined. Relationships between composite's crack opening displacement, constitutive properties, woven parameters, and damage state are established. Experimental crack opening displacements of cracking modes III and V in a two-dimensional plain-woven melt-infiltration silicon carbide fiber-reinforced silicon carbide composite from the published literature are predicted. For cracking mode III with partial interface debonding, the crack opening displacement increased nonlinearly with applied stress; and for cracking mode V with complete interface debonding, the crack opening displacement increased linearly with applied stress.

Bending fatigue behavior in an advanced SiC/SiC ceramic matrix composite component at elevated temperature in air

The present study aims to understand the high-temperature bending fatigue behavior at the stress-concentrated Y-shape junction of a component made of Tyranno SA3 fiber/BN interphase/SiC matrix composite. The SiC/SiC CMC component was processed via a hybrid technique by combining Chemical Vapor Infiltration (CVI) and Polymer Impregnation and Pyrolysis (PIP) processes. Two different types of tests, namely, point-load-bending-static-test and point-load-bending-fatigue-test, were performed at 1100 °C. The point-load-bending-static test revealed quasi-ductile or shear failure owing to the lower elastic modulus of the PIP-SiC matrix. The first matrix-cracking occurred when the high-stress region reached approximately 180 MPa, which was facilitated by the pores and cracks that remained after the PIP process around the intricate Y-shape junction of the sample. The point-load-bending-fatigue tests were performed under the maximum of the fatigue stresses ranging from 180 to 290 MPa. When the maximum of the fatigue stress was lower than 60% of the static strength, multiple matrix-cracking were pronounced such that the component did not fail and withstand 1000 fatigue cycles. At higher stresses of 250 and 290 MPa, delamination due to shear stress generation at the fiber tows interface and degradation of the BN interphase ultimately led to the fracture of the component at low fatigue cycles of less than 100. Moreover, the fracture morphology of the 290-MPa-fatigue sample showed brittle failure, which was due to matrix-crack-assisted oxygen embrittlement. In addition, a brief comparison between the point-load-bending-fatigue test and the conventional tension-compression fatigue test was discussed.

Effect of multiple matrix cracking on crack bridging of fiber reinforced engineered cementitious composite

In the present paper, a modified micromechanics based model that describes the crack bridging stress in randomly oriented discontinuous fiber reinforced engineered cementitious composite is developed. In the model, effect of multiple matrix cracking on fiber embedded length, which in turn influencing fiber bridging in the composite, is taken into consideration. First, crack spacing of high strength-low shrinkage engineered cementitious composite was experimentally determined by photographing the specimen surface at some given loading points during uniaxial tensile test. The diagram of average cracking spacing and loading time of each composite is obtained based on above data. Then, fiber bridging model is modified by introducing a revised fiber embedment length as a function of crack spacing. The model is verified with uniaxial tensile test on both tensile strength and crack opening. Good agreement between model and test results is obtained. The modified model can be used in design and prediction of tensile properties of fiber reinforced cementitious composites with characteristics of multiple matrix cracking.

In-situ observation of damage in unidirectional CMC laminates under tension

We observe microscopic damage progression in un-notched unidirectional SiC–SiC ceramic matrix composite laminates loaded monotonically in tension. In situ tensile testing was conducted in air at room temperature and combined with X-ray tomography imaging. The unidirectional specimens tested were novel double-reduced dogbones designed to develop matrix cracks in the synchrotron field of view. Multiple matrix cracks that rapidly traversed the section of each specimen were observed through the volume until the specimens broke into two pieces. The details of each matrix crack were tracked at each stress increment to better understand how the cracks evolve under load. One of the unidirectional specimens contains a matrix crack that displays a sharp 90° turn along the fiber direction in its final crack path. Fiber breaks were observed and several fibers in the unidirectional specimen showed multiple breaks. Fiber break opening was measured for each fiber break and the average fiber break opening for each stress increment is reported. The location and pullout distance of fiber breaks surrounding a matrix crack, as well as matrix crack spacing, are of modeling interest and are reported.

Relationship Between Matrix Cracking and Delamination in CFRP Cross-Ply Laminates Subjected to Low Velocity Impact.

The effect of matrix cracking on the delamination morphology inside carbon fiber reinforced plastics (CFRP) laminates during low-velocity impact (LVI) is an open question. In this paper, the relationship between matrix cracking and delamination is studied by using cross-ply laminates. Several methods, including micrograph, C-scan, and visual inspection, were adopted to characterize the damage after LVI experiments. Based on the experimental results, finite element (FE) models were established to analyze the damage mechanisms. The matrix cracking was predicted by the extended finite element method (XFEM) and the Puck criteria, while the delamination was modeled by cohesive elements. It was revealed that the matrix crack in the bottom ply not only promoted the outward propagation of delamination but also contributed to the narrow delamination beneath the impact location. Multiple matrix cracks occurred in the middle ply. The ones close to the plate center initiated the delamination and prevented large-scale delamination beneath the impact location. For the cracks that were far away, no significant effect on delamination was found. In conclusion, the stress redistribution caused by the crack opening determines the delamination.

Effect of Cyclic Fatigue Loading on Matrix Multiple Fracture of Fiber-Reinforced Ceramic-Matrix Composites

In this paper, the effect of cyclic fatigue loading on matrix multiple fracture of fiber-reinforced ceramic-matrix composites (CMCs) is investigated using the critical matrix strain energy (CMSE) criterion. The relationships between multiple matrix cracking, cyclic fatigue peak stress, fiber/matrix interface wear, and debonding are established. The effects of fiber volume fraction, fiber/matrix interface shear stress, and applied cycle number on matrix multiple fracture and fiber/matrix interface debonding and interface wear are discussed. Comparisons of multiple matrix cracking with/without cyclic fatigue loading are analyzed. The experimental matrix cracking of unidirectional SiC/CAS, SiC/SiC, SiC/Borosilicate, and mini-SiC/SiC composites with/without cyclic fatigue loading are predicted.

Synergistic effects of fiber/matrix interface wear and fibers fracture on matrix multiple cracking in fiber-reinforced ceramic-matrix composites

ABSTRACTIn this paper, the synergistic effects of fiber/matrix interface wear and fibers fracture on matrix multiple cracking in fiber-reinforced ceramic-matrix composites (CMCs) are investigated using the critical matrix strain energy (CMSE) criterion. The shear-lag model combined with the fiber/matrix interface wear model, fibers fracture model and the fiber/matrix interface fracture mechanics debonding criterion is adopted to analyze the fiber and matrix axial stress distribution inside of the damaged composite. The relationships between the matrix multiple cracking, fatigue peak stress, applied cyclic number, fiber/matrix interface wear and debonding and fibers failure are established. The effects of fiber volume fraction, fiber/matrix interface shear stress, fiber/matrix interface debonded energy, cycle number, fatigue peak stress and fibers strength on matrix multiple cracking evolution are discussed. Comparisons of matrix multiple cracking with/without cyclic fatigue loading are analyzed. The experimental multiple matrix cracking of unidirectional SiC/CAS, SiC/CAS-II, SiC/Borosilicate and mini-SiC/SiC composites with/without cyclic fatigue loading are predicted.

Coupled stress and energy criterion for multiple matrix cracking in cross-ply composite laminates

Transverse cracking, i.e. matrix cracking in the off-axis plies of the laminate, is widely recognized as the first damage mode to appear in continuous fibre-reinforced composite laminates subjected to in-plane loading. Since transverse cracking has a great influence on the subsequent damage steps such as delaminations or oblique cracks, it is important to be able to predict its onset and growth accurately. In this paper, it is proposed to use a combination of the Coupled Criterion of Finite Fracture Mechanics (FFM) and the Equivalent Constraint Model (ECM) to predict the evolution of crack density with increasing applied load. Two formulations – a discrete formulation and a continuous formulation – are developed for the energy criterion within the Coupled Criterion. Some dependences between the two formulations are proved, which justifies the good agreement found by the models based on continuous formulations presented by other authors despite the inherent discrete nature of the phenomenon. Dependence of the failure load predicted by the Coupled Criterion on the layer thickness ratio and brittleness number (a structural parameter that characterizes a combination of the stiffness, strength, fracture toughness and the thickness of the cracked ply of the laminate) is examined and discussed for carbon/epoxy and glass/epoxy laminates. Finally, a comparison against experimental results shows a good agreement.

Two-way bending behaviour of hollow concrete block masonry walls reinforced by composite materials

Abstract This paper presents an experimental study devoted to investigating the effectiveness of externally bonded composites to improve the out-of-plane behaviour of masonry walls. Two strengthening materials were used that were chosen deliberately from more environmentally friendly composites: a flax fibre reinforced polymer and a glass textile reinforced cementitious matrix. Five masonry walls were tested under two-way bending: one reference, three reinforced and one repaired. Special attention was paid to the anchorage of the strengthening bands to the masonry. The performance of each strengthening configuration was estimated by considering the out-of-plane load capacity, ductility, energy dissipation and crack pattern. It appears that all of the tested specimens, whatever the strengthening materials, developed a substantial increase (from 20% to 30%) in their out-of-plane load capacity and exhibited ductility and displacement capacity. The transversal anchor systems proved to be effective (and readily achievable). From the results obtained in this study, it is concluded that the multiple matrix cracks in the glass textile-reinforced mortar allow a more extensive stress redistribution that makes this material a promising solution for the out-of-plane strengthening of masonry walls. An analytical approach, based on a cross-section analysis, is introduced to calculate the load-carrying capacity of the strengthened walls and a satisfactory agreement is obtained between experimental and theoretical results.

The effects of matrix cracks on the nonlinear vibration characteristics of shear deformable laminated beams containing carbon nanotube reinforced composite layers

This paper deals with the effect of matrix cracks on the free and forced vibration characteristics of a shear deformable laminated beam which contains carbon nanotube reinforced composite (CNTRC) layers. Two matrix-cracked models, namely self-consistent model (SCM) and elasticity theory model (ETM), are selected to describe the degraded stiffness of the beam. The beam rests on a two-parameter elastic foundation in thermal environments. Based on a higher order shear deformation theory and von Kármán nonlinear strain-displacement relationships, the motion equations are established and solved by means of a two-step perturbation approach. The material properties of both fiber reinforced composite (FRC) layers and CNTRC layers are assumed to be temperature-dependent. The effects of the crack density, CNT volume fraction, temperature variation, as well as the foundation stiffness on the dynamic responses of hybrid laminated beams with multiple matrix cracks are discussed in detail.

Tensile deformation behavior of tungsten fibre-reinforced tungsten composite specimens in as-fabricated state

To overcome the inherent brittleness of tungsten, which is a promising candidate for a plasma-facing material in a future fusion device, tungsten fibre-reinforced tungsten composites (Wf/W) have been developed. As a part of the materials characterisation program on Wf/W, we present the results of first tensile tests of as-fabricated Wf/W in this contribution. The results give insight on the ultimate tensile strength properties and reveal the active toughening mechanisms under tension load within the composite. Fibre bridging, fibre necking as well as fibre pull out were observed. This is leading to the typical pseudo ductile behavior of the composite which is characterized by a rising load bearing capability despite multiple matrix cracks accompanied by non catastrophic crack propagation (in the matrix). The description of the mechanical tests is supplemented by detailed microstructural investigations.

Nonlinear low-velocity impact analysis of matrix cracked hybrid laminated plates containing CNTRC layers resting on visco-Pasternak foundation

Abstract This paper investigates the low-velocity impact response of a shear deformable laminated plate which contains both carbon nanotube reinforced composite (CNTRC) layers and fiber reinforced composite (FRC) layers. The effect of matrix cracks is considered and a refined self-consistent model (SCM) is selected to describe the degraded stiffness of the plate. The material properties of both FRC layers and CNTRC layers are assumed to be temperature-dependent. The plate rests on a visco-Pasternak foundation in thermal environments. A modified Hertz model is utilized to describe the contact force between the impactor and the plate. Based on a higher order shear deformation theory and von Karman nonlinear strain-displacement relationships, the motion equations of the plate are established and solved by means of a two-step perturbation approach. The effects of the crack density, CNT volume fraction, temperature variation and the foundation stiffness on the nonlinear low-velocity impact response of hybrid laminated plates with multiple matrix cracks are discussed in detail.

Comparisons of Damage Evolution between 2D C/SiC and SiC/SiC Ceramic-Matrix Composites under Tension-Tension Cyclic Fatigue Loading at Room and Elevated Temperatures.

In this paper, comparisons of damage evolution between 2D C/SiC and SiC/SiC ceramic-matrix composites (CMCs) under tension–tension cyclic fatigue loading at room and elevated temperatures have been investigated. Fatigue hysteresis loops models considering multiple matrix cracking modes in 2D CMCs have been developed based on the damage mechanism of fiber sliding relative to the matrix in the interface debonded region. The relationships between the fatigue hysteresis loops, fatigue hysteresis dissipated energy, fatigue peak stress, matrix multiple cracking modes, and interface shear stress have been established. The effects of fiber volume fraction, fatigue peak stress and matrix cracking mode proportion on fatigue hysteresis dissipated energy and interface debonding and sliding have been analyzed. The experimental fatigue hysteresis dissipated energy of 2D C/SiC and SiC/SiC composites at room temperature, 550 °C, 800 °C, and 1100 °C in air, and 1200 °C in vacuum corresponding to different fatigue peak stresses and cycle numbers have been analyzed. The interface shear stress degradation rate has been obtained through comparing the experimental fatigue hysteresis dissipated energy with theoretical values. Fatigue damage evolution in C/SiC and SiC/SiC composites has been compared using damage parameters of fatigue hysteresis dissipated energy and interface shear stress degradation rate. It was found that the interface shear stress degradation rate increases at elevated temperature in air compared with that at room temperature, decreases with increasing loading frequency at room temperature, and increases with increasing fatigue peak stress at room and elevated temperatures.

The effects of matrix cracks on the nonlinear bending and thermal postbuckling of shear deformable laminated beams containing carbon nanotube reinforced composite layers and piezoelectric fiber reinforced composite layers

Abstract This paper investigates the effect of matrix cracks on the nonlinear bending and thermal postbuckling of a piezoelectric shear deformable laminated beam which contains both carbon nanotube reinforced composite (CNTRC) layers and piezoelectric fiber reinforced composite (PFRC) layers. Two matrix-cracked models, namely self-consistent model (SCM) and elasticity theory model (ETM), are selected to describe the degraded stiffness of carbon fiber reinforced composite (CFRC) layers. The beam rests on a two-parameter elastic foundation in thermal environments. Based on a higher order shear deformation theory and von Karman nonlinear strain-displacement relationships, the governing equations are established and solved by means of a two-step perturbation approach. The beam-foundation interaction and thermal effects are also included. The material properties of all layers used are assumed to be temperature-dependent. The effects of the density of matrix crack, CNT volume fraction, temperature variation, the foundation stiffness as well as applied voltage on the nonlinear bending and thermal postbuckling behavior of hybrid laminated beams with multiple matrix cracks are discussed in detail.

Modeling cyclic fatigue hysteresis loops of 2D woven ceramic-matrix composite at elevated temperatures in air considering multiple matrix cracking modes

In this paper, the cyclic fatigue hysteresis loops of 2D woven SiC/SiC ceramic-matrix composites (CMCs) at elevated temperatures has been investigated. The interface slip between fibers and the matrix existed in the matrix cracking mode 3 and mode 5, in which matrix cracking and interface debonding occurred in the longitudinal yarns, are considered as the major reason for hysteresis loops of 2D woven CMCs. The hysteresis loops of 2D SiC/SiC composite corresponding to different peak stresses, test conditions and loading frequencies have been predicted using present analysis. The damage parameter, i.e., the proportion of matrix cracking mode 3 in the entire matrix cracking modes of the composite, and the hysteresis dissipated energy increase with increasing fatigue peak stress. With increasing cycle number, the interface shear stress in the longitudinal yarns decreases, leading to transition of interface slip types of matrix cracking mode 3 and mode 5.

Modeling the Effect of Multiple Matrix Cracking Modes on Cyclic Hysteresis Loops of 2D Woven Ceramic-Matrix Composites

In this paper, the effect of multiple matrix cracking modes on cyclic loading/unloading hysteresis loops of 2D woven ceramic-matrix composites (CMCs) has been investigated. The interface slip between fibers and the matrix existed in matrix cracking mode 3 and mode 5, in which matrix cracking and interface debonding occurred in longitudinal yarns, are considered as the major reason for hysteresis loops of 2D woven CMCs. The effects of fiber volume content, peak stress, matrix crack spacing, interface properties, matrix cracking mode proportion and interface wear on interface slip and hysteresis loops have been analyzed. The cyclic loading/unloading hysteresis loops of 2D woven SiC/SiC composite corresponding to different peak stresses have been predicted using the present analysis. It was found that the damage parameter, i.e., the proportion of matrix cracking mode 3 in the entire cracking modes of the composite, increases with increasing peak stress.