Micromechanical Damage Research Articles

Statistical micromechanical damage model for SH-SFRC under tensile load considering the interfacial slip-softening and matrix spalling effects

Strain hardening behavior can be observed in steel fiber reinforced concretes under tensile loads. In this paper, a statistical micromechanical damage framework is presented for the strain hardening steel fiber reinforced concrete (SH-SFRC) considering the interfacial slip-softening and matrix spalling effects. With a linear slip-softening interface law, an analytical model is developed for the single steel fiber pullout behavior. The crack bridging effects are reached by averaging the contribution of the fibers with different inclined angles. Afterwards, the traditional snubbing factor is modified by considering the fiber snubbing and the matrix spalling effects. By adopting the Weibull distribution, a statistical micromechanical damage model is established with the fracture mechanics based cracking criteria and the stress transfer distance. The comparison with the experimental results demonstrates that the proposed framework is capable of reproducing the SH-SFRC’s uniaxial tensile behavior well. Moreover, the impact of the interfacial slip-softening and matrix spalling effects are further discussed with the presented framework.

Strain response of fiber-reinforced ceramic-matrix composites subjected to stress-rupture with stochastic load at intermediate temperature

To ensure the reliability and safety of ceramic-matrix composites (CMCs) hot-section components used in the aero engines, it is necessary to perform the strain response of CMCs at intermediate temperatures (600 to 1000 °C) under stress-rupture with stochastic loading. In this paper, the strain response of SiC/SiC composite under stress-rupture with stochastic load at intermediate temperatures is investigated. Multiple damage mechanisms of matrix cracking, interface debonding and oxidation, and fiber’s oxidation and fracture are considered. Matrix crack spacing, interface oxidation and debonding length, fiber’s broken probability, and intact fiber’s stress are determined using micromechanical damage models. Experimental strain response and internal damage evolution of SiC/SiC composite under constant and stochastic stress are predicted. Effects of stochastic stress level and stochastic time, material properties, damage state and environment temperature on composite’s strain response and stress-rupture life are discussed. When stochastic stress level and environment temperature increase, the composite’s strain at the stochastic stress increases, the time for the interface complete debonding and oxidation decreases, and the stress-rupture life decreases.

Micro-mechanical damage of needle puncture on bovine annulus fibrosus fibrils studied using polarization-resolved Second Harmonic Generation(P-SHG) microscopy

Needle injection has been widely used in spinal therapeutic or diagnostic processes, such as discography. The use of needles has been suspected in causing mild disc degeneration which can lead to long-term back pain. However, the localised microscopic damage caused by needles has not been well studied. The local progressive damage on a microscopic level caused by needle punctures on the surface of bovine annulus fibrosus was investigated. Four different sizes of needle were used for the puncture and twenty-nine bovine intervertebral discs were studied. Polarization-resolved second harmonic generation and fluorescent microscopy were used to study the local microscopic structural changes in collagen and cell nuclei due to needle damage. Repeated 70 cyclic loadings at ±5% of axial strain were applied after the needle puncture in order to assess progressive damage caused by the needle. Puncture damage on annulus fibrosus were observed either collagen fibre bundles being pushed aside, being cut through or combination of both with part being lift or pushed in. The progressive damage was found less relevant to the needle size and more progressive damage was only observed using the larger needle. Two distinct populations of collagen, in which one was relatively more organised than the other population, were observed especially after the puncture from skewed distribution of polarization-SHG analysis. Cell shape was found rounder near the puncture site where collagen fibres were damaged.

Micro-mechanical fracture dynamics and damage modelling in brittle materials.

This study explores the interplay between wave propagation and damage in brittle materials. The damage models, based on micro-mechanical fracture dynamics, capture any possible unstable growth of micro-cracks, introducing a macroscopic loss of stability. After stating the non-dimensional mathematical problem describing the wave propagation with damage, we introduce a non-dimensional number, called the microscopic evolution index, which links the micro and macro scales and discriminates the microscopic scale behaviour. For large values of microscopic evolution index, corresponding to a microscopic quasi-static process coupled with a macroscopic dynamic one, the macroscopic dynamic system could lose its hyperbolicity or become very stiff and generate shock waves. A semi-analytical solution to the one-dimensional wave propagation problem with damage, which could be very useful in the accuracy evaluation of the numerical schemes, was constructed. Concerning the asymptotic behaviour of the dynamic exact solution on the microscopic evolution index (or on the strain rate), an important strain rate sensitivity was found: the pulse loses its amplitude for decreasing strain rate and, starting with a critical value, the micro-scale model is rate independent. A possible regularization technique to smooth the shock waves at low and moderate strain rates is discussed. Finally, some numerical results analyse the role played by the the friction on the micro-cracks in the damage modelling of blast wave propagation. This article is part of the theme issue 'Fracture dynamics of solid materials: from particles to the globe'.

Observing progressive damage in carbon fiber epoxy laminate composites via 3D in-situ X-ray tomography

As the use of fiber-reinforced polymer composites grows in aerospace structures, there is an emerging need to implement damage tolerant approaches. The use of in-situ synchrotron X-ray tomography enables direct observations of progressive damage relative to the microstructural features, which are studied in a T650/5320 laminate composite with two layups via monotonic tension. Specifically, the interactions of micromechanical damage mechanisms at the notch tip were analyzed through 3D image processing as the crack grew. The analysis showed intralaminar cracking was dominant during crack initiation, delamination became prevalent during the later stages of crack progression, and fiber breakage was, in general, largely related to intralaminar cracking.

Damage micromechanisms of stress corrosion cracking in Al-Mg alloy with high magnesium content

Al-10Mg alloys, which are highly susceptible to SCC, were prepared with various β precipitate morphologies. Interrupted in-situ tensile tests were conducted under synchrotron X-ray radiation, employing a recently developed X-ray microtomography technique that combines high-energy, applicability to metallic materials, and ultra-high resolution. Preferential dissolution of the β phase along grain boundaries, and incidental intergranular and transgranular fracture, were observed in 3D. A drastic decrease in SCC resistance was measured after hydrogen charging. The additional effect of external hydrogen absorbed from an aqueous solution during loading was also revealed, by directly measuring crack-tip plasticity. The aquatic environment, one of the most extreme conditions for hydrogen uptake, caused continuous crack-tip corrosion. Catastrophic failure was observed when an alloy had both a relatively high areal grain boundary coverage by film-like β phase, and a reticulately interconnected plate-like β phase in the grain interior. Hydrogen bubble formation was also observed, in relation to the progress of crack-tip corrosion. The main corrosion product was identified as Al(OH)3, based on its linear absorption coefficient. The respective amounts of corrosion products and hydrogen gas in the gas bubbles, and the pH value of the aqueous solution, were accurately measured during in-situ tensile testing, enabling estimation of the local elevation of hydrogen content in the crack-tip vicinity. Finally, a quantitative criterion for the occurrence of hydrogen embrittlement in inter-β ligaments is discussed, together with the applicability of the findings to the prevention of SCC.

In situ strength analysis of cross‐ply composite laminates containing defects and interleaved woven layer using a computational micromechanics approach

AbstractThe transverse strength of 90° plies located in cross‐ply laminates subjected to transverse tension is investigated numerically. To reach this aim, it is assumed that the transverse cracking is formed by coalescence of fiber–matrix debonding, which propagates along the planes parallel to the fibers. The two‐dimensional finite element model (FEM) investigates the dominant micromechanical damage mechanisms, fiber–matrix debonding, and matrix cracking using the cohesive zone model (CZM) and plasticity, respectively. The numerical simulation is according to the extended computational micromechanics (ECMM) approach, which can be applied as a useful virtual test method instead of performing costly characterization tests. The results obtained from the present study show that the defects such as voids, imperfections, and residual stresses contribute to reducing the in situ strength of 90° plies. In the case of using an interleaved woven layer, the formation of the first transverse crack in unit cells within 90° layer is delayed.

In situ synchrotron computed tomography study of nanoscale interlaminar reinforcement and thin-ply effects on damage progression in composite laminates

In situ X-ray synchrotron radiation computed tomography (SRCT) of carbon fiber composite laminates reveals the first-ever qualitative and quantitative comparisons of 3D progressive damage effects introduced by two mechanical enhancement technologies: aligned nanoscale fiber interlaminar reinforcement and thin-ply layers. The technologies were studied individually and in combination, using aerospace-grade unidirectional prepreg standard-thickness (‘std-ply’) and thin-ply composite laminates. The relatively weak interlaminar regions of the laminates were reinforced with high densities of aligned carbon nanotubes (A-CNTs) in a hierarchical architecture termed ‘nanostitching’. Quasi-isotropic double edge-notched tension (DENT) laminates were tested and simultaneously 3D-imaged via SRCT at various load steps, revealing a progressive 3D network of damage micro-mechanisms that were segmented according to modality and extent. For load steps of 0%, 70%, 80%, and 90% of baseline ultimate tensile strength (UTS), intralaminar matrix cracking and fiber/matrix interfacial debonding are found to be the dominant damage mechanisms, common to all laminate types. For both std-ply and thin-ply, nanostitched laminates had qualitatively and quantitatively similar matrix damage modality and extent compared to the baseline laminates through 90% UTS, including relatively few delaminations, despite an ~9% increase in std-ply nanostitched UTS over the std-ply baseline. Complementary finite element-based modeling of damage predicts greater delamination extent in std-ply vs. thin-ply laminates that manifests only between 90% and 100% UTS, offering an explanation for the observed positive nanostitch effect in the std-ply, which is known to be more susceptible to delamination formation and growth than the thin-ply laminates. Thin-ply, with and without nanostitch, intrinsically suppresses matrix damage, as expected from past work and evidenced here by 6.5X less overall matrix damage surface area vs. std-ply baseline laminates averaged over all load steps. These findings contribute new insights from high-resolution experimental mapping of composite damage states that can guide and inform mechanical enhancement approaches and improved damage models.

Effects of overload mode-mixity on fatigue damage behavior and governing micromechanisms in AA7075 under biaxial fatigue loading

An investigation into the effects of overload mode-mixity on crack growth behavior and governing micromechanisms of AA7075 T6 has been conducted. Cruciform AA7075 T6 specimens were subjected to constant amplitude planar biaxial fatigue with single overloads, and key fatigue damage behavior, including fatigue life, crack growth rate, and recovery distance, were investigated and correlated to overload parameters. Additionally, SEM fractography was conducted to identify and relate fracture surface features to governing fatigue damage micromechanisms. An increase in fatigue life was observed for all cases of mode-mixity, with the minimum increase occurring at 45°. The mix-mode overloads also caused crack retardation in all cases. In the shear dominant overloads, however, initial post-overload crack acceleration occurred and was immediately followed by crack retardation. Microscale analysis showed distinct fracture features in the pre-overload, transient, and post-overload regions for both tensile and shear dominant overloads.

Α numerical evaluation of various damage models for thermoplastic composite materials subjected to quasi-static tensile loading

In the present work, damage propagation in thermoplastic composite laminates subjected to quasi-static tensile loading was numerically simulated using different damage models. The simulation was performed using the commercial finite element suite LS-Dyna, where various material models were evaluated based on their ability to simulate the thermoplastic composite behavior. More specifically, material models based on Tsai-Wu failure criteria (MAT_055), progressive damage modeling (MAT_162), micromechanical material modeling (MAT_215) and continuum damage modeling (MAT_261) were implemented, comparing the output failure strength and load – displacement curve with experimental data available in the literature. The approach of damage evolution and failure type for each model was taken under consideration as well. Overall, the progressive damage model (MAT_162) presented the most accurate prediction of the material’s failure behavior.

Perturbed First Order State Dependent Moreau's Sweeping Process

In this paper, we deal with the state-dependent nonconvex sweeping process motivated through quasi-variational inequalities arising in the evolution of sandpiles, quasistatic evolution problems with friction, micromechanical damage models for iron materials. We prove the existence of absolutely continuous solution for the problem in presence of a perturbation, that is an external force applied on the system. The perturbation considered here is general and take the form of a sum of a single-valued Carath'eodory mapping and a set-valued unbounded mapping.

Coupling of X‐ray computed tomography and surface in situ analysis combined with digital image correlation method to study low cycle fatigue damage micromechanisms in lost foam casting A319 alloy

AbstractAn experimental protocol has been set up in order to study the low cycle fatigue (LCF) damage micromechanisms in a lost foam casting (LFC) A319 alloy at room temperature. The microstructure of the alloy was characterized by using X‐ray computed tomography (X‐ray CT) prior to the LCF tests performed with surface in situ observations using a long distance microscope, which allow crack initiation and propagation being tracked in real‐time. The mechanical fields measured by digital image correlation (DIC) method allowed establishing the relations between strain localizations, damage evolutions and microstructure while a developed etching method, which gives a natural texture to the surface, makes DIC feasible to an acceptable resolution without masking the microstructure. The results showed that crack initiation is ascribed to strain localizations induced by large pore and/or the propagation of a previously nucleated crack. Cracks propagate along hard inclusions but the orientation of hard inclusions has also an influence on crack path.

Verification of a cohesive model‐based extended finite element method for ductile crack propagation

AbstractIn this study, an approach utilizing a conjunction of the extended finite element method (XFEM) and the Gurson‐Tvergaard‐Needleman (GTN) micromechanical damage model is proposed for predicting the ductile crack propagation of a mill‐annealed Ti‐6Al‐4V alloy. The cohesive model‐based XFEM approach is used to capture the continuous crack propagation process, and the GTN model is applied to describe the constitutive behaviour of the material. Simulations are conducted by using the standard finite element code ABAQUS following a Newton–Raphson algorithm solution with employing the user material subroutine of the GTN model. In comparison with the experimentalresults of the smooth, notched and cracked titanium specimens, this approach is shown to be an efficient method for simulating the ductile crack propagation process under different stress triaxialities.

Extended mean-field homogenization of viscoelastic-viscoplastic polymer composites undergoing hybrid progressive degradation induced by interface debonding and matrix ductile damage

In this contribution, a probabilistic micromechanics damage framework is presented to predict the macroscopic stress–strain response and progressive damage in unidirectional glass-reinforced thermoplastic polymer composites. Motivated by different failure modes observed experimentally, the damage mechanism in the vicinity of the fibers (namely, the interphase) is characterized by initiating and growing voids. The mechanisms can be formulated through a Weibull probabilistic density function. In contrast, the ductile progressive degradation of matrix initial stiffness is analyzed via the continuum damage theory. To accommodate different damage mechanisms in the matrix and the interphase, a three-phase Mori-Tanaka (MT) method and transformation field analysis approach (TFA) are established within a unified framework that allows simulation of both ductile and discrete damages in different phases. Moreover, the rate-dependent viscoelastic and viscoplastic response of the polymer matrix phase is modelled through a phenomenological model consisting of four Kelvin-Voigt branches and a viscoplastic branch under the thermodynamics framework. The reliability and efficiency of the modified mean-field damage model, based on TFA and Mori-Tanaka scheme, are assessed by comparing the simulated stress-strain response against full-field Abaqus simulations under both unidirectional and multiaxial nonproportional loading paths at different loading rates. The developed model provides an efficient alternative to the finite-element based full-field homogenization schemes or other mean-field micromechanics techniques that may be compared, as well as a framework for a potential extension of the theory for simulating damage evolution in composites with random reinforcement orientations.

Detection of Microdefects on the Surfaces of Corroded Steel Pipes

The micromechanisms of biocorrosion damage to specimens of 17G1S-U pipe steel are studied on the basis of a combination of the profilometry approaches with fracture mechanics. We develop new methods for the numerical analysis of stress concentration factors regarded as parameters of localization of the microscopic concentrators of corrosion stresses. The improved approach is applied to the analysis of profilograms of corroded pipe steel. The possibility of appearance of safe (admissible) corrosion defects is substantiated with regard for the stress concentration in the vicinities of microscopic notches corresponding to depressions in the profilograms.

Parameter studies on the mineral boundary strength influencing the fracturing of the crystalline rock based on a novel Grain-Based Model

The grain-based model (GBM) in two-dimensional Particle Flow Code (PFC2D) is widely employed to investigate the mechanical response characteristics of crystalline rocks under external load considering the realistic petrographic texture. However, due to the poor self-locking effect of the Parallel-Bond (PB) inside the minerals and unreasonable parametric assignment for the Smooth-Joint (SJ) at the mineral boundaries, the original GBM cannot reproduce the exact microcracking process of brittle rocks. To solve the problem, the novel grain-based model (nGBM) composed of the Flat-Joint (FJ) and the SJ was proposed in our previous research, which not only enhances the rotational resistance of particles, but also improves the simulation of the mineral boundaries. In this study, the nGBM was carefully established and calibrated based on the properties of Alxa porphyritic granite. A series of simulation tests of uniaxial compression, triaxial compression and direct tension under different mineral boundary parametric conditions were carried out to observe the deformation, microcracking and failure behaviors of the nGBM. Quantitative analyses of the mineral boundary properties and the mechanical behaviors of the numerical specimen revealed the extremely complicated relationships between them, which can help explain the micromechanical damage process of crystalline rocks and provide valuable reference for the model calibration.

Micromechanical damage behavior of fiber-reinforced composites under transverse loading including fiber-matrix debonding and matrix cracks

This paper examines the micromechanical damage behavior of carbon-epoxy composite using representative volume elements (RVEs). An algorithm is developed to generate random distributions of fibers in the RVE, and it is possible to create a fiber distribution with high fiber volume fractions. Fiber-matrix debonding and matrix crack are considered as the dominant damage modes. The fiber material is considered linear elastic and Drucker–Prager’s plastic criterion coupled with progressive damage behavior is assumed for matrix material. Moreover, cohesive elements are considered to model fiber-matrix debonding. The effects of different parameters such as fiber volume fraction, random fiber distribution, normal radii distribution, various cohesive parameters, and minimum fiber neighboring spacing on the overall damage behavior of the RVE, mostly the regime beyond the peak stress, are described in detail. It is concluded that due to the high-stress concentration regions, smaller elements are needed to analyze the high fiber volume fractions RVEs accurately. The peak stress and the corresponding strain are insensitive to microstructural randomness. Furthermore, the RVEs’ final failure strain is highly dependent on different fiber arrangements layouts. Since the RVEs are under transverse strain, normal cohesive strength is the dominant cohesive zone parameter that has a significant role in the damage behavior of RVEs. It is shown that minimum fiber neighboring spacing affects the strain in which matrix crack initiates.

A micromechanical tension-compression fatigue hysteresis loops model of fiber-reinforced ceramic-matrix composites

In this paper, a micromechanical tension-compression fatigue hysteresis loops model of fiber-reinforced ceramic-matrix composites (CMCs) is developed. Upon unloading or reloading, the stress-strain of tension-compression fatigue hysteresis loops are divided into three different regions. Multiple micromechanical damage parameters of unloading transition stress, closure stress of the matrix cracking, compressive transition stress, complete compressive stress, and reloading transition stress are adopted to characterize the tension-compression stress-strain hysteresis loops. The characteristics of the tension-compression fatigue hysteresis loops of unidirectional SiC/CAS composite are analyzed for different material properties, damage stage, tensile fatigue peak stress, and compression fatigue valley stress. The experimental tension-tension and tension-compression fatigue stress-strain hysteresis loops of unidirectional SiC/CAS composite are predicted using the developed micromechanical models. Under low fatigue valley compressive stress, the tension-compression fatigue hysteresis loop exhibits no closure of matrix cracking; and under high fatigue valley compressive stress, the tension-compression fatigue hysteresis loops exhibit closure of matrix cracking, and complete compressive in the fiber and the matrix. However, the compressive valley stress has no effect on the values of matrix cracking closure stress, compressive transition stress, and complete compressive stress.

Sheet Molding Compound Automotive Component Reliability Using a Micromechanical Damage Approach

The mastering of product reliability is essential for industrial competitiveness. If for metallic materials the topic is well-known, especially in automotive industry, Original Equipment Manufacturers are expecting strong support of their suppliers to full-fill the lack data. This paper presents a new original approach, using a micromechanical based on damage model to address the problem of reliability of Sheet Molding Compound (SMC) components. The first part demonstrates the inadequacy of the standard method of reliability on SMC material through its application on the new Peugeot 3008. In fact, the very flat S-N curve of SMC, and in general, composite materials is not appropriate for acceleration effect. The proposed model correlates the stress, damage and strength with both cycle number and slamming velocity. It emphasizes the relation between the effective distribution with the slamming velocity effect. Then, a new reliability approach based on a micromechanical fatigue/damage model was developed. The definition of new probability distributions based on damage was necessary to apply properly the stress-resistance approach. It allows taking into account the velocity effect by switching in damage space. Finally, applying this new methodology on the Peugeot 3008, leads to the definition of the optimal validation laboratory tests to ensure the reliability. Indeed, the required number of cycles to ensure reliability has been reduced significantly. Micromechanical damage reliability approach could be an efficient way to ensure the reliability of short fiber reinforcement composite components used in industrial context.

A Micromechanical Fatigue Limit Stress Model of Fiber-Reinforced Ceramic-Matrix Composites under Stochastic Overloading Stress.

Fatigue limit stress is a key design parameter for the structure fatigue design of composite materials. In this paper, a micromechanical fatigue limit stress model of fiber-reinforced ceramic-matrix composites (CMCs) subjected to stochastic overloading stress is developed. The fatigue limit stress of different carbon fiber-reinforced silicon carbide (C/SiC) composites (i.e., unidirectional (UD), cross-ply (CP), 2D, 2.5D, and 3D C/SiC) is predicted based on the micromechanical fatigue damage models and fatigue failure criterion. Under cyclic fatigue loading, the fatigue damage and fracture under stochastic overloading stress at different applied cycle numbers are characterized using two parameters of fatigue life decreasing rate and broken fiber fraction. The relationships between the fatigue life decreasing rate, stochastic overloading stress level and corresponding occurrence applied cycle number, and broken fiber fraction are analyzed. Under the same stochastic overloading stress level, the fatigue life decreasing rate increases with the occurrence applied cycle of stochastic overloading, and thus, is the highest for the cross-ply C/SiC composite and lowest for the 2.5D C/SiC composite. Among the UD, 2D, and 3D C/SiC composites, at the initial stage of cyclic fatigue loading, under the same stochastic overloading stress, the fatigue life decreasing rate of the 3D C/SiC is the highest; however, with the increasing applied cycle number, the fatigue life decreasing rate of the UD C/SiC composite is the highest. The broken fiber fraction increases when stochastic overloading stress occurs, and the difference of the broken fiber fraction between the fatigue limit stress and stochastic overloading stress level increases with the occurrence applied cycle.