Matrix Crack Initiation Research Articles

Progressive damage and stiffness degradation assessments of double‐lap CFRP/Ti interference fit bolted joints under quasi‐static tensile load

AbstractMatrix crack propagation and stiffness degradation behaviors of the carbon fiber reinforced polymer/titanium alloy (CFRP/Ti) bolted joint were characterized by a synergistic damage mechanics approach. The parametric study including pre‐tightening torques and interference fit sizes was conducted. The results showed that the joint stiffness degradation exhibited characteristics of local stiffness degradation due to local stress concentration. Stiffness degradation in different plies was caused by matrix crack damage occurring in different directions. The pre‐tightening torque significantly increased the joint stiffness and restrain matrix crack progression, effectively inhibiting the stiffness degradation of the joint. Moreover, the low interference fit level delayed the crack initiation in −45° ply and 45° ply and the crack propagation of the laminate, while promoted the crack initiation in 90° ply. The stiffness degradation of the laminate could be significantly reduced by interference fit.Highlights Matrix crack propagation and stiffness degradation behaviors of the CFRP laminate were characterized by a synergistic damage mechanics method. A FE model of the CFRP/Ti double‐lap interference fit bolted joint was established. Influences of pre‐tightening torques on both matrix crack initiation and propagation were investigated. The optimum interference fit size of the matrix damage strengthening was 0.20%–0.60%.

Microscopic damage behavior in CFRP cross-ply laminates at cryogenic temperature

For the practical use of cryogenic propellant tanks made of CFRP laminates, experimental elucidation of the laminates’ microstructural damage propagation behavior at cryogenic temperatures is important. This paper presents a newly developed tensile test rig that enables in-situ observation of microscopic damage using an optical microscope at cryogenic temperatures using a Gifford–McMahon refrigerator. In-situ observations of microscopic damage under uniaxial tensile loading were done at room temperature (290 K, 17 °C) and at 30 K (−243 °C) on cross-ply thin-ply CFRP specimens of three kinds with different 90° layer thicknesses. The results demonstrated that the crack propagation behavior is independent of temperature, that the matrix crack density is higher, and that the onset of matrix crack initiation strain is lower at 30 K than at 290 K. Furthermore, the thermal strain within 90° layer at 30 K and at 290 K was estimated using finite element analyses (FEA). The FEA results suggest that the decrease in onset strain of matrix crack initiation at 30 K is mainly attributed to the increase in the thermal strains within the 90° layer.

Dynamic response of ultra-high performance engineered cementitious composites (UHP-ECC) under low-velocity impact: Effect of waste rubber incorporation and low temperatures

This study aims to explore the dynamic response of ultra-high performance engineered cementitious composites (UHP-ECC) incorporating waste crumb rubber (CR) at various temperatures, focusing on its potential to enhance the resilience and sustainability of civil infrastructures against low-velocity impacts. To date, the impact behaviour of UHP-ECC under low temperatures has rarely been explored. Firstly, natural river sand and waste tyre CR was utilized to prepare the UHP-ECC. Then, a series of mechanical tests, including compression test, flexural test and uniaxial tensile test were carried out to investigate the static mechanical properties of rubberised UHP-ECCs. In addition, the effects of different waste CR incorporations (0%, 5%, 10%, and 15%) and various temperatures (25 °C, −5 °C, −30 °C, −50 °C, −100 °C and −196 °C) were comprehensively investigated by low-velocity impact tests with constant impact energy. Lastly, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) model was introduced to evaluate the overall performance of UHP-ECC. It was found that the use of river sand and CR significantly enhanced the tensile ductility and impact toughness of UHP-ECC. Impact energy primarily dissipates through damage such as matrix crack initiation, propagation, and fibre pull-out/rupture within the specimen. Adding CR notably decreased stress fluctuations during impact at room temperature, facilitating steady state energy absorption. Moreover, the time to reach peak impact force decreased with decreasing temperature across all UHP-ECC groups. At room temperature during impact process, fibre failure mode is dominated by pull-out failure, while lower temperatures lead to increased fibre rupture at the cracking surface. In low-temperature conditions, the impact response of rubberised UHP-ECC necessitates a comprehensive consideration of the synergistic effects, including material contraction, fibre bridging capacity, rubber phase transition, and water freezing.

Tensile damage evolution and mechanical behaviour of SiCf/SiC mini-composites through 4D in-situ micro-CT and data-driven modelling

Damage evolution of SiCf/SiC ceramic matrix mini-composites (CMMCs) was characterised by using a 4D in-situ micro-computed tomography (CT) tensile test and digital volume correlation (DVC) technique. Additionally, a CT damage data-driven shear lag model was developed to predict its tensile stress-strain response. A 4D in-situ X-ray CT tensile test of a unidirectional SiCf/SiC mini-composite was first carried out. Then two ad-hoc deep-learning image segmentation models were developed to automatically identify its microstructure and damages induced by tension, respectively. Damage evolution was quantitively characterised by visualising the initiation and propagation of matrix cracks in three-dimensions (3D). A two-step approach was employed to evaluate its 3D internal strain distributions at various loading levels, which further revealed strain concentrations and helped establishing the tensile stress-strain response of the CMMCs. It was observed that transverse cracking is the predominant damage mode, and the average crack opening displacement increases with loading. A high-fidelity X-ray CT data-driven shear lag model was developed, incorporating inputs of transverse matrix crack spacing calculated by the 4D in-situ CT test data. The predicted stress-strain response showed a good correlation with the experimental results.

A damage model for matrix cracks in composite laminates under fatigue loading based on continuum damage mechanics

A damage model for transverse matrix cracks in composite laminates under fatigue loading was presented in this paper. The model was prosed based on the theory of continuum damage mechanics (CDM) at macro level and could capture the ‘edge effect’ of matrix cracks in composite laminate under fatigue loading. To obtain the constitutive equation of UD lamina containing transverse matrix cracks, a polynomial Gibbs free energy function was derived, and a macro damage parameter was introduced to characterize the influence of matrix cracks on multidirectional stiffness properties of UD composite. To predict the initiation and evolution of matrix cracks, a previously deduced initial crack initiation life function and a Paris-like equation in terms of damage driving force were employed, respectively. Prediction results of two cross-ply laminates under fatigue loading with different stress levels were compared to the experimental results and prediction results obtained from previously proposed model. The comparison results indicate the presented model is more effective and reliable in predicting the initiation and evolution of matrix cracks and the corresponding stiffness degradation in composite laminates under fatigue loading.

In-plane shear experimental method and mechanical behavior of ceramic matrix mini-composites

In-plane shear mechanical experiments of ceramic matrix mini-composites (CMMC) were realized in this paper by overcoming the difficulties of material preparation, specimen design, gripping and loading, deformation measurement, etc. The in-plane shear stress-strain responses of different matrix volume fractions were obtained based on the method. The stress-strain response of CMMC was strongly non-linear, and its elastic modulus and strength were positively correlated to the matrix volume fraction. The main factors affecting the digital image correlation (DIC) based micro-region shear deformation measurement are analyzed quantitatively, and the corresponding solutions are discussed. The DIC calculation time model is established, and the accurate estimation of DIC processing time is realized. The shear strain field evolution clearly captured the matrix crack initiation and propagation.

Experimental investigation of carbon long fiber reinforced polyamide 6 exposed to environmental conditions

AbstractTo enhance the possibilities in lightweight constructions in terms of processability and recyclability, fiber reinforced thermoplastics are a promising class of materials. In this context, the fiber‐matrix interface has a major influence on the mechanical properties of the composite. With polyamide 6 (PA6) being a hygroscopic thermoplastic, the effects of elevated humidity and temperature on the mechanical behavior must be considered [1]. This study aims to characterize the micro‐mechanical material properties of carbon long fiber reinforced PA6 in quasi‐static tensile tests after exposure to elevated temperature and humidity levels. Therefore, the specimens are conditioned in different climates and tested afterwards. In order to determine the initiation and propagation of matrix cracks, interface failure, and fiber fracture, the experiments are conducted on a micro‐scale with an average cross‐section of 0.03 mm2. The damage patterns are captured using optical microscopy and SEM images. The effects of conditioning at various temperature and humidity levels are discussed. The main results are the qualitative description of the degradation of mechanical properties due to hydrothermal effects.

Matrix cracking of 2D SiC/SiC composite characterized by in situ SEM and nano-CT

Two-dimensional plain-woven silicon carbide (SiC) fiber-reinforced SiC matrix (2D SiC/SiC) composite was prepared by polymer infiltration-pyrolysis (PIP). Matrix cracking mechanisms of the composite were investigated by in situ SEM and nano-CT to grasp tensile damage evolution. Results showed that PIP-SiC matrix possessed low-fracture energy with non-homogeneous distribution, leading to simultaneous initiation of matrix cracking outside transverse fiber bundles and in unreinforced regions. Cracks then got deflected along weak fiber/matrix interface, which accelerated crack proliferation within the composite. With an increase in the stress, cracks subsequently deflected along plain-woven layers and converged to form longitudinal macrocracks. The composite was finally delaminated via sliding.

Automatic simulation of the initiation and propagation of interface cracks and matrix cracks with VCFEM

Based on the transformation mechanism of interfacial cracks propagating into a matrix, this paper proposes a model containing the particle phase, interphase, matrix phase, interface cracks, and matrix cracks. The model derives the functional, and we develop a new Voronoi cell finite element method (VCFEM) containing the interphase to describe interface crack and matrix crack initiation and propagation. A new mesh-subdivision method reflecting crack propagation from the interface to the matrix is constructed, which can automatically simulate the initiation and propagation of interface cracks and the transformation and penetration of interface cracks into matrix cracks. With crack propagation, various combined elements models are proposed. For these combined elements, their shared external nodes change as the cracks propagate through the original element, while the external node numbers of other elements remain unchanged. The effectiveness of the proposed method is verified by comparing the results of the new VCFEM with those obtained with Abaqus and analytical solution through several numerical examples. Since the proposed method assumes a high-order stress field within an element and can capture the stress concentration with fewer elements, it is suitable for large-scale calculation.

Predicting fatigue damage in composites subjected to general loading conditions

A computationally efficient fatigue analysis methodology is proposed that uses a cycle jump approach to drive the accumulation of fatigue damage and a unified local fatigue cohesive zone model that can predict the initiation and propagation of cracks using a reduced set of model parameters. A new definition of the stress ratio is proposed for general loading conditions, which include negative load ratios, unsynchronized loads, and problems where the mode mixity changes during a cycle. The cycle jump procedure was verified by performing analyses of standard double cantilever beam and mixed mode bending tests. Then, the model was validated by performing analyses of double notch shear tests and initiation of transverse matrix cracking in a [0/90] laminate using models that account for residual thermal stresses. The results indicate that the analysis methodology can reproduce experimentally measured fatigue damage initiation and evolution for a variety of different configurations and load combinations.(Keywords: C. Cohesive interface modelling, B Fatigue, B. Delamination, A. Polymer-matrix composites (PMCs))

A reduced-input cohesive zone model with regularized extended finite element method for fatigue analysis of laminated composites in Abaqus

A cohesive zone model (CZM) for fatigue crack propagation was integrated within the Regularized eXtended Finite Element Method (Rx-FEM) discrete damage modeling framework. This CZM constitutive model, which is formulated in terms of S-N stress-life curves rather than the more usual rates of crack propagation described with a Paris law, can predict both crack initiation and propagation by relying on the intrinsic relationships between S-N and the Paris law. This feature of the model is of significant practical interest since S-N curves can be synthesized with few parameters and simple engineering assumptions, while the experimental characterization of the Paris law parameters for all required stress ratios, mode mixities, and material interfaces in a composite structure is very difficult and often impractical. Used in combination with the Rx-FEM method, this CZM can predict mesh-independent crack networks in composite structures subjected to cyclic or quasi-static loads. The Rx-FEM methodology for fatigue damage was implemented in Abaqus using two superimposed sets of standard Abaqus elements to represent the enriched displacement field. The capabilities of the proposed methodology are demonstrated by comparing the experimental and predicted response of a mixed-mode bending (MMB) test, as well as a Clamped Tapered Beam (CTB) sub-element designed to study matrix crack initiation, delamination propagation, and subsequent delamination migration from one ply interface to another.

Modeling creep behavior in ceramic matrix composites

In this work, a three-dimensional viscoplasticity formulation with progressive damage is developed and used to investigate the complex time-dependent constituent load transfer and progressive damage behavior in ceramic matrix composites (CMCs) subjected to creep. The viscoplasticity formulation is based on Hill's orthotropic plastic potential, an associative flow rule, and the Norton-Bailey creep power law with Arrhenius temperature dependence. A fracture mechanics-informed isotropic matrix damage model is used to account for CMC brittle matrix damage initiation and propagation, in which two scalar damage variables capture the effects of matrix porosity as well as matrix property degradation due to matrix crack initiation and propagation. The Curtin progressive fiber damage model is utilized to simulate progressive fiber failure. The creep-damage formulation is subsequently implemented as a constitutive model in the generalized method of cells (GMC) micromechanics formulation to simulate time-dependent deformation and material damage under creep loading conditions. The developed framework is used to simulate creep of single fiber SiC/SiC microcomposites. Simulation results are in excellent agreement with experimental and numerical data available in the literature.

Prediction of matrix crack initiation and evolution and their effect on the stiffness of laminates with off-axis plies under in-plane loading

A model is described which allows the exact calculation of stresses in a cracked ply under combined state of strain. Closed form expressions for the stresses in each ply are combined in an energy density-based criterion to predict crack spacing and the resulting transverse modulus and shear modulus. Inelastic effects due to non-linearities of the ply-level shear stress-strain curve are accounted for through computation of the permanent shear strain in the ply. The model accounts for ply thickness, stacking sequence and load redistribution effects of a relatively broad class of laminates. Comparisons with test results for a variety of laminates and materials show very good to excellent agreement. The approach developed is extremely efficient and can easily be incorporated in numerical progressive failure analysis, where the stiffness properties of each element can be updated every time the crack pattern changes and in fatigue analysis where the stiffness of a ply or a laminate can be determined during every load cycle.

Matrix cracking initiation, propagation and laminate failure in multiple plies of general symmetric composite laminates

This paper formulates an analytical model based on intrinsic material properties to predict ply cracking initiation and propagation in multiple plies and its impact on laminate strength in general symmetric laminates (possibly made of thin-plies) under combined triaxial normal loads and in-plane and out-of-plane shear loads while the effect of thermal residual stresses and statistical distribution of fracture energies are considered. To do so, a novel complete homogenization technique combined with recently developed accurate stress transfer models is implemented in conjunction with multi-axial energy-based failure criteria, Monte Carlo type of simulation and a strain-based fiber failure criterion. The model predictions show very good agreement with experimental results.

A bi-directional damage model for matrix cracking evolution in composite laminates under fatigue loadings

An analytical model for prediction of transverse matrix cracks in composite laminates under fatigue loading was proposed. The micromechanics method was utilized to characterize the damaged behavior of composite laminates. The initial matrix crack initiation life was defined and deduced based on micromechanics method. Then the relation between initial matrix crack initiation life and critical energy release rate was established to obtain the distribution of initial matrix crack initiation life in cracked plies, and the evolution of matrix crack density and stiffness degradation were predicted. The prediction results were compared with experimental results and the comparison shows good agreement.

Predicting the effects of microstructure on matrix crack initiation in fiber reinforced ceramic matrix composites via machine learning

A reduced-order, data-driven, probabilistic predictive model to quantify damage initiation in continuous SiC ceramic fiber SiC ceramic matrix composites (CMCs) at pertinent lengths scales using machine learning tools is proposed and explored. A novel framework is developed to characterize the influence of key stochastic microstructure attributes on matrix crack initiation. The approach is illustrated for the case of transverse crack initiation in the matrix surrounding fibers oriented perpendicular to the loading direction. A variety of stochastic microstructure attributes were considered including fiber spacing, fiber diameter, and coating thickness. Statistics of a commercial CMC microstructure were digitally represented and used to instantiate microstructures. In addition, discrete digital instantiations generated over a range of the distributed microstructural attributes were considered. The statistics of the distributed microstructure attributes were quantified using n-point statistics and reduced using principal component analysis. The elastic responses of the instantiated microstructures were characterized using finite element analysis (FEA). Results from the FEA were used as the ground truth to calibrate and validate a data-driven machine learning (ML) model. The quantified stochastic microstructure attributes were correlated with the statistics of the simulated damage response. The predictive capabilities of the model for a new microstructure class were demonstrated.

Matrix and interface cracking in cross-ply composite structural battery under combined electrochemical and mechanical loading

In this paper propagation of matrix cracks and debonds at the coating/matrix interface in the 90°-layer of a cross-ply structural composite battery are studied numerically. The structural composite battery consists of micro-battery units, made of a solid electrolyte coated carbon fiber embedded in an electrochemically active polymer matrix. During charging the fiber swells and the matrix shrinks leading to high stresses on the fiber/matrix scale and to anisotropic free expansion of the composite ply. Two load cases are considered, pure electrochemical load (intercalation) and combined electrochemical and thermomechanical load. Energy release rates (ERR) of radial matrix cracks along two potential propagation paths are calculated using 2-D finite element models of the transverse plane in a cross-ply laminate with a square packing of fibers in the 90°-ply and using homogenized 0°-ply. Results show that the matrix crack growth towards the nearest fiber is unstable, and that the debond crack growth is in mixed mode. For a cross-ply structural battery composite the sequence of macro-scale crack forming events differs from a conventional cross-ply composite, as well as for a UD composite battery laminate. The most likely course of failure events in a cross-ply laminate are: 1) vertical radial matrix crack initiation and unstable growth; 2) debond is initiated at certain length of the matrix crack.

Impact of process induced residual stresses on interlaminar fracture toughness in carbon epoxy composites

Residual stresses are induced in composite laminates during the process of manufacturing due to thermal mismatch between composite constituents during curing. Processes induced residual stresses effects the safety of structural components and can play a main role in matrix cracking, crack initiation and propagation. The objective of this research is to study the influence induced residual stresses on interlaminar fracture toughness (GI) of Carbon/Epoxy laminates. Initially laminates were cured under room temperature followed by post curing at various temperatures using a chosen cure cycle. Slitting method was employed to determine the residual stress distribution in post cured laminates and its effects on GI was estimated using Double Cantilever beam (DCB) test. The results show a gradual increase in GI with increase in compressive residual stresses in composite laminate. Further, the fracture surfaces of laminates were carefully studied using scanning electron microscope to know the interfacial adhesion of matrix and fiber.

Investigation of the Tensile Fracture Behavior of Notched C/SiC Composite Using <i>In Situ</i> SEM and Micro-CT

In order to better understand the failure mechanism of C/SiC composites, the tensile behavior of notched C/SiC composites was investigated by the in-situ scanning electron microscopy (SEM) and the micro-CT technique. Surface morphologies of the C/SiC sample during tensile loading were in-situ observed by SEM, while the three-dimensional microscopic images of the C/SiC sample before loading and after failure were obtained by micro-CT. The results showed that no cracks formed in the initial elastic stage corresponding to the linear part of the load-displacement curve. However, corresponding to the following non-linear part of the load-displacement curve, matrix crack initiation, fiber pull-out, crack propagation and deflection appeared consecutively in the notched region of the sample. What’s more, different crack growth paths existed in different directions of the sample during tensile failure. In general, approximately flat fracture formed in the plying direction and serrated or stepped fracture were observed in the needling direction. It indicated that the in-situ observation method combining SEM and micro-CT can obtain the micro-structure images of the material in different states, which is helpful to analyze the fracture failure mechanism of composites.

Calculation of stress intensity factors of matrix crack tip in particle reinforced composites using the singular Voronoi cell finite element method

In this paper, a new singular Voronoi cell finite element method (S-VCFEM) is proposed to study the initiation and propagation of interfacial debonding and matrix cracking in particulate reinforced composite. Composites with large-scale inclusions and cracks can be easily simulated with this model. A new assumed stress hybrid variational functional is derived from the element energy function to accommodate the interface traction reciprocity on bonded interface and the interface traction-free on debonded interface and matrix crack surface. S-VCFEM is achieved through enhancements in stress functions in the assumed stress hybrid formulation. In addition to polynomial terms and interaction terms, singular stress terms of Williams expansion are added for stress functions, which are adaptively enriched to accurately capture the crack-tip stress concentrations. After obtaining the stress field, calculation of stress intensity factors is performed, using the least square method based on stress value obtained numerically in the S-VCFEM. The efficiency of the method is verified against numerical results obtained by ABAQUS with XFEM module for the same problem considering a matrix-crack and a debonded interface.