Hysteresis loops of fiber-reinforced ceramic-matrix composites under in-phase/out-of-phase thermomechanical and isothermal cyclic loading

In this paper, the stress?strain hysteresis loops of fiber-reinforced ceramic-matrix composites (CMCs) under in-phase/out-of-phase thermomechanical and isothermal cyclic loading have been investigated. The thermomechanical hysteresis loops models have been developed considering synergistic effects of thermal temperature cycling, stress levels and fiber/matrix interface debonding. The relationships between thermal cyclic temperatures, peak stress, fiber/matrix interface shear stress and stress?strain hysteresis loops under in-phase/out-of-phase thermomechanical and isothermal cyclic loading have been established. The effects of fiber volume fraction, peak stress, matrix crack spacing, interface frictional coefficient, interface debonded energy and temperature range on the stress?strain hysteresis loops under in-phase/out-of-phase thermomechanical and isothermal cyclic loading have been analyzed. The hysteresis loops of cross-ply SiC/magnesium aluminosilicate (MAS) composite under in-phase/out-of-phase thermomechanical and isothermal fatigue loading have been predicted.     

Growth of interfacial debonding in notched two-dimensional unidirectional composite under stress and displacement controls

A simplified calculation method for study of the growth of interfacial debonding between elastic fiber and elastic matrix ahead of the notch-tip in composites under displacement and stress controlled conditions was presented based on the shear lag approach in which the influences of residual stress and frictional shear stress at the debonded interface were incorporated. The calculation method was applied to a model two-dimensional composite. An outline is given of the difference and similarity in the growing behavior of the debonding between the displacement and stress controls, and of the influences of the residual stresses, frictional shear stress, the nature of the final cut component (fiber or matrix) and sample length on the debonding behavior.     

Effects of residual stress and interfacial frictional shear stress on interfacial debonding at notch-tip in two-dimensional unidirectional composite

A calculation method based on the shear lag approach was presented to get an approximate estimate of influences of residual stresses and frictional shear stress at the debonded interface on the interfacial debonding behavior at the notch-tip along fiber direction in two-dimensional unidirectional double-edge-notched composites. With this method, the energy release rate for initiation and growth of debonding as a function of composite stress were calculated for some examples. The calculation results showed in outline how much the tensile and compressive residual stresses in the matrix and fiber along fiber direction, respectively, act to hasten the initiation and growth of the debonding when the final cut element in the notch is matrix, while they act to retard them when the final cut element is fiber, and how much the frictional shear stress at the debonded interface reduces the growth rate of the debonding.     

Comparisons of interface shear stress degradation rate between C/SiC and SiC/SiC ceramic-matrix composites under cyclic fatigue loading at room and elevated temperatures

The interface shear stress in C/SiC and SiC/SiC ceramic-matrix composites with different fiber preforms, i.e. unidirectional, cross-ply, 2D woven, 2.5D woven, and 3D braided, under cyclic fatigue loading at room and elevated temperatures have been estimated. An effective coefficient of the fiber volume fraction along the loading direction was introduced to describe the fiber preforms. Based on fiber slipping mechanisms, the hysteresis loops models considering different interface slip cases have been developed. Using the experimental fatigue hysteresis dissipated energy, the interface shear stress degradation rates of C/SiC and SiC/SiC composites with different fiber preforms at room and elevated temperatures have been obtained and compared. It was found that the interface shear stress degradation rate is the highest for 3D braided SiC/SiC at 1300 °C in air, and the lowest for 2D woven C/SiC at room temperature under cyclic fatigue loading.     

In situ observation of interfacial debonding process induced by matrix crack propagation in two-dimensional unidirectional model composites

Interfacial debonding behavior is studied for unidirectional fiber reinforced composites from both experimental and analytical viewpoints. A new type of two-dimensional unidirectional model composite is prepared using 10 boron fibers and transparent epoxy resin with two levels of interfacial strength. In situ observation of the internal mesoscopic fracture process is carried out using the single edge notched specimen under static loading. The matrix crack propagation, the interfacial debonding growth and the interaction between them are directly observed in detail. As a result, the interfacial debonding is clearly accelerated in specimens with weakly bonded fibers in comparison with those with strongly bonded fibers. Secondary, three-dimensional finite element analysis is carried out in order to reproduce the interfacial debonding behavior. The experimentally observed relation between the mesoscopic fracture process and the applied load is given as the boundary condition. We successfully evaluate the mode II interfacial debonding toughness and the effect of interfacial frictional shear stress on the apparent mode II energy release rate separately by employing the present model composite in combination with the finite element analysis. The true mode II interfacial debonding toughness for weaker interface is about 0.4 times as high as that for a stronger interface. The effect of the interfacial frictional shear stress on the apparent mode II energy release rate for the weak interface is about 0.07 times as high as that for the strong interface. The interfacial frictional shear stress and the coefficient of friction for weak interface are calculated as 0.25 and 0.4 times as high as those for strong interface, respectively.     

Stress transfer around a broken fiber in unidirectional fiber-reinforced composites considering matrix damage evolution and interface slipping

A shear-lag model is applied to study the stress transfer around a broken fiber within unidirectional fiber-reinforced composites(FRC) subjected to uniaxial tensile loading along the fiber direction.The matrix damage and interfacial debonding,which are the main failure modes,are considered in the model.The maximum stress criterion with the linear damage evolution theory is used for the matrix.The slipping friction stress is considered in the interfacial debonding region using Coulomb friction theory,in whic...     

Damage monitor and life prediction of carbon fiber-reinforced ceramic-matrix composites at room and elevated temperatures using hysteresis dissipated energy-based damage parameter

In this paper, the damage monitor and life prediction of carbon fiber-reinforced ceramic-matrix composites (C/SiC CMCs) have been investigated using the hysteresis dissipated energy-based damage parameter. The evolution of the interface shear stress, hysteresis dissipated energy, hysteresis dissipated energy-based damage parameter and the broken fibers fraction vs. cycle number, the fatigue life S?N curves of unidirectional, cross-ply and 2.5D C/SiC composites at room temperature and 800 °C in air atmosphere have been analyzed. For unidirectional C/SiC, the hysteresis dissipated energy and hysteresis dissipated energy-based damage parameter first increase and then decrease with cycle number, and the fatigue limit stress decreases from 88% tensile strength at room temperature to 20% of the tensile strength at 800 °C in air atmosphere; for cross-ply C/SiC, the hysteresis dissipated energy and hysteresis dissipated energy-based damage parameter decrease with increasing applied cycles, and the fatigue limit stress decreases from 85% tensile strength at room temperature to 22% tensile strength at 800 °C in air; and for 2.5D C/SiC, the hysteresis dissipated energy and hysteresis dissipated energy-based damage parameter increases with cycle number, and the fatigue limit stress decreases from 70% tensile strength at room temperature to 25% tensile strength at 800 °C in air.     

Evaluation on the interfacial fracture toughness of fiber-reinforced titanium matrix composites by push out test

The models for single-fiber push out test are developed to evaluate the fracture toughness G_IIc of the fiber/matrix interface in titanium alloys reinforced by SiC monofilaments. The models are based on fracture mechanics, taking into consideration of the free-end surface and Poisson expansion. Theoretical solutions to G_IIc are obtained, and the effects of several key factors such as the initial crack length, crack length, friction coefficient, and interfacial frictional shear stress are discussed. The predictions by the models are compared with the previous finite element analysis results for the interfacial toughness of the composites including Sigma1240/Ti-6-4, SCS/Ti-6-4, SCS/Timetal 834, and SCS/Timetal 21s. The results show that the models can reliably predict the interfacial toughness of the titanium matrix composites, in which interfacial debonding usually occurs at the bottom of the samples.     

Hardening and softening during fatigue fracture

Summary The comparison of the change of hardness and plastic deformation amplitude at a constant stress loading or stress amplitude at a constant deformation loading during the fatigue process shows some singularity of the hardening and softening effects. These effects were investigated on mean carbon and low-alloyed steel and on globular cast iron.The fatigue fractures at cycle numbers 10⁴÷10⁶ under stresses below the yield strength predominate in the softening process, which arises after an inconsiderable hardness increase extends in the region to 0·2 from the fracturing cycle number. Under the stresses above the yield strength, which in some cases for annealed and coarse-grained states are below the fatigue limit, the hardening process predominates, followed by a hardness increase in the field up to 0·25 and above the fracturing cycle number.At low cycle fatigue fractures with cycle numbers < 10⁴ depending on the cyclic plastic properties of steels the fatigue process can be followed by a continuous hardening or softening till fracture. This process is characterized by the change of the deformation amplitude and a one-sided accumulation of plastic deformations at a constant amplitude of active stresses. The one-sided accumulation of deformations commonly ends in a quasistatic failure. Under loading with a constant deformation amplitude during softening a fatigue fracture takes place as a result of damage accumulation under the alternating stresses with amplitudes decreasing with cycle number.     

Effect of interfacial debonding and matrix cracking on mechanical properties of multidirectional composites

In composites, debonding at the fiber–matrix interface and matrix cracking due to loading or residual stresses can effect the mechanical properties. Here three different architectures — 3-directional orthogonal, 3-directional 8-harness satin weave and 4-directional in-plane multidirectional composites — are investigated and their effective properties are determined for different volume fractions using unit cell modeling with appropriate periodic boundary conditions. A cohesive zone model (CZM) has been used to simulate the interfacial debonding, and an octahedral shear stress failure criterion is used for the matrix cracking. The debonding and matrix cracking have significant effect on the mechanical properties of the composite. As strain increases, debonding increases, which produces a significant reduction in all the moduli of the composite. In the presence of residual stresses, debonding and resulting deterioration in properties occurs at much lower strains. Debonding accompanied with matrix cracking leads to further deterioration in the properties. The interfacial strength has a significant effect on debonding initiation and mechanical properties in the absence of residual stresses, whereas, in the presence of residual stresses, there is no effect on mechanical properties. A comparison of predicted results with experimental results shows that, while the tensile moduli E ₁₁, E ₃₃and shear modulus G ₁₂ match well, the predicted shear modulus G ₁₃ is much lower.     

Nanomechanical modeling of interfaces of polyvinyl alcohol (PVA)/clay nanocomposite

Abstract

We study interfacial debonding of several representative structures of polyvinyl alcohol (PVA)/pyrophillite-clay systems – both gallery-interface (polymer/clay interface in the interlayer region containing polymer between clay layers stacked parallel to each other) and matrix-interphase (polymer/clay interphase-region when individual clay layers are well separated and dispersed in the polymer matrix) – using molecular dynamics simulations, while explicitly accounting for shearing/sliding (i.e. Mode-II) deformation mode. Ten nanocomposite geometries (five 2-D periodic structures for tension and five 1-D periodic structures for shearing) were constructed to quantify the structure-property relations by varying the number density of polymer chains, length of polymer chains and model dimensions related to the interface deformation. The results were subsequently mapped into a cohesive traction–separation law, including evaluation of peak traction and work of separation that are used to characterise the interface load transfer for larger length scale micromechanical models. Results suggest that under a crack nucleation opening mode (i.e. Mode-I), the matrix-interphase exhibits noticeably greater strength and a greater work of separation compared to the gallery-interface; however, they were similar under the shearing/sliding mode of deformation. When compared to shearing/sliding, the tensile peak opening mode stresses were considerably greater but the displacement at the peak stress, the displacement at the final failure and the work of separation were considerably lower. Results also suggest that PVA/clay nanocomposites with higher degree of exfoliation compared with nanocomposites with higher clay-intercalation can potentially display higher strength under tension-dominated loading for a given clay volume fraction.     

Theoretical analysis and numerical simulation of development length of straight steel fiber in cementitious materials

In fiber-reinforced concrete, it is important to choose an appropriate length in each fiber to develop its full yield strength without a failure in the bond strength between the fiber and the concrete. This length is called the fiber development length, L_df. The bond capacity is evaluated between the fiber and the concrete using the pull-out tests. This test evaluates the bond capacity of various types of steel fiber surfaces relative to a specific embedded length. If the steel fiber is smooth and straight, the distribution of tensile stresses will be uniform around the fiber at a specific section and varies along the anchorage length of the fiber and at a radial distance from the surface of the fiber. Pull-out tests can be performed on an embedded straight steel fiber in concrete matrix, in this case, the tensile force, P, is increased gradually and the number of cracks and their spacings and widths is recorded. The bond stresses vary along the fiber length between the cracks. The strain in the steel fiber is maximum at the cracked section and decreases toward the middle section between cracks. If the embedded length of the straight steel fiber is greater than the development length, the steel fiber may yield, leaving some length of the fiber in the concrete. The linear elastic behavior of the fiber-matrix system is interrupted by interface debonding which occurs due to overall weak bonding between the concrete matrix and the surface of the steel fiber. This paper introduces new developed shear lag model and explains simplified method to find the development length of straight steel fiber in concrete matrix using finite element model and analysis of shear lag stresses, where the maximum tension force which is applied on the steel fiber is resisted by another internal force related with the ultimate average bond stress, steel fiber diameter and its yield strength.     

Is there any contradiction between the stress and energy failure criteria in micromechanical tests? Part II. Crack propagation: Effect of friction on force-displacement curves

In micromechanical tests for estimating fiber-matrix interfacial properties, such as the pull-out and microbond tests, fiber debonding from a matrix is often accompanied by friction in debonded areas. In the present study, force-displacement curves, which are usually recorded in these tests, were modeled with taking interfacial friction into consideration. The friction stress was assumed, as a first approximation, to be constant across the interface. Two different approaches to interfacial failure were used: the shear-lag approach with a stress-based debonding criterion (the ultimate interfacial shear strength) and the linear elastic fracture mechanics approach using the critical energy release rate as a condition for crack propagation. The force-displacement curves derived from both models are in good agreement with each other and with experimental micromechanical data. It was shown that any pull-out and microbond experiment comprises four stages: (1) linear loading up to the point where debonding starts; (2) stable crack propagation with friction-controlled debonding; (3) catastrophic debonding; and (4) post-debonding friction. Stable crack propagation was shown to be controlled by both friction and release of residual thermal stresses. An algorithm for estimating both fiber-matrix adhesion and interfacial friction from the microbond and pull-out tests data has been proposed.     

Stress transfer efficiency in model composites under dynamic loading

The micromechanics of tension–tension fatigue loading in model single-fibre composite geometries is investigated in this paper. In an attempt to emulate the conditions encountered in full carbon fibre composites, the fibres were prestrained prior to the curing process to ensure that they were free of high residual compressive stresses as a result of resin shrinkage. The resulting specimens were grouped into two categories depending on the level of the initial fibre prestrain (case A low, case B high). The cyclic load is designed to be well below the endurance fatigue limit of the polymer matrix (∼0.6%), and to have a frequency low enough to avoid unwanted thermal post curing. Throughout the preparation procedure, as well as during fatigue loading, the fibre stress (strain) was constantly monitored by means of laser Raman spectroscopy. The fibre axial stress distributions at each fatigue step were converted to interfacial shear stress (ISS) distributions, from which important parameters such as the maximum ISS the system can accommodate, the transfer length for efficient stress built-up and the length required for the attainment of maximum ISS were obtained. The results showed that, up to 2×10⁶ loading cycles, the main parameters which affected the stress transfer efficiency at the interface were the fibre fracture process itself and the viscoelastic behaviour of the matrix material. Received: 7 November 2001 / Accepted: 22 March 2002 / Published online: 5 July 2002     

Modified null field method for elastic wave scattering from a partially debonded fiber-SH-waves

Debonded fibers influence the macro-mechanical behavior of fiber-reinforced composite materials. Debonded fibers contribute to the initiation and growth of cracks at the fiber/matrix interface. To examine such problems, the scattering of elastic SH-waves (problem of anti-plane strain) from debonded fibers is studied with a numerical method which can handle the mixed boundary conditions on the partially bonded fiber. A modification of the null field of T-matrix method is developed for this purpose. The modification is achieved by the introduction of a mathematical surface. The simultaneous solution of the integral representations of the field scattered by the mathematical surface and the actual fiber surface give rise to sufficient equations that permit solution of the debonded fiber problem. The scattering cross-section and the far field amplitude are calculated as a function of frequency, fiber properties and debonding area. This will be of interest in structural applications where such cross-sections can be used to compute the dynamical effective properties of damaged composites.     

单晶铝在拉压循环过程中形成的两种位错组态与成因

研究了［１１０］和［１００］取向高纯铝单晶在６×１０^－4拉压疲劳应变振幅条件下的应力σ_m和内耗Ｑ^－１的变化，对不同阶段的位错组态作了详细的透射电子显微镜观察，并利用滑移几何的观点予以解释 关键词：     

Grain boundary engineering: fatigue fracture

Abstract

Grain boundary engineering has revealed significant enhancement of material properties by modifying the populations and connectivity of different types of grain boundaries within the polycrystals. The character and connectivity of grain boundaries in polycrystalline microstructures control the corrosion and mechanical behaviour of materials. A comprehensive review of the previous researches has been carried out to understand this philosophy. Present research thoroughly explores the effect of total strain amplitude on phase transformation, fatigue fracture features, grain size, annealing twinning, different grain connectivity and grain boundary network after strain controlled low cycle fatigue deformation of austenitic stainless steel under ambient temperature. Electron backscatter diffraction technique has been used extensively to investigate the grain boundary characteristics and morphologies. The nominal variation of strain amplitude through cyclic plastic deformation is quantitatively demonstrated completely in connection with the grain boundary microstructure and fractographic features to reveal the mechanism of fatigue fracture of polycrystalline austenite. The extent of boundary modifications has been found to be a function of the number of applied loading cycles and strain amplitudes. It is also investigated that cyclic plasticity induced martensitic transformation strongly influences grain boundary characteristics and modifications of the material’s microstructure/microtexture as a function of strain amplitudes. The experimental results presented here suggest a path to grain boundary engineering during fatigue fracture of austenite polycrystals.     

Effect of substrate dimensions on dynamics of ultrasonic consolidation

An FEM model is developed for a fundamental study of the time-dependent mechanical behavior of the substrate and its dimensions on ultrasonic consolidation. The simulation shows that for a given vibration condition, the amplitude of contact friction stress and displacement stabilizes to a saturated state after certain number of ultrasonic cycles. With the increased substrate height, the amplitude of contact frictional stress decreases, while that of contact interface displacement increases. The reason for the decrease in the frictional stress at the contact interface for certain substrate heights is the complicated wave interference occurring in the substrate. An analytical wave model has been built to validate the FEM model. A specific substrate geometry (height:width = 1.0) generates a minimum frictional strain state at the interface as a result of wave superposition. Such minimum strain state is believed to have produced the “lack of bonding” defect for the geometry. The energy density and transfer coefficient at the contact interface with different substrate heights is used as an indicator to correlate with the bond formation in ultrasonic bonding.     

不同时效状态的含铜4%的铝合金在疲劳载荷下溶质原子与位错的交互作用

为了进一步研究在疲劳载荷下含铜4％的铝合金中的位错钉扎过程,进行了经过不同时效的试样的扭转疲劳试验,测定了经过各种应力循环数N以后的滞后迴线的形状和面积,从而算出了在每次循环中的能量消耗ΔE和最大抗扭矩T_m。所选择的时效温度和时效时间是使试样中分别有G.P.[1]区,G.P.[2]区,θ′相和稳定的θ相出现。把所得的ΔE-N曲线和T_m-N曲线的变化情况作比较时可以看出,在疲劳载荷的起始阶段引起位错钉扎的并不是由于相变产物如G.P.[1]或[2]区的作用。比较并分析了在各种时效状态下的第一周能量消耗值(ΔE)₁的变化,结果指出,在所研究的铝铜合金的情形,产生ΔE的原因是由于在位错附近的点阵中有起伏的内应力场出现,因为位错在这种内应力场中往复运动需要作功。产生这种起伏的应力场的因素有点缺陷(空位和溶质原子)、原子簇、G.P.[1]区和G.P.[2]区,或者其他种不在位错线上聚集或成核的缺陷。根据上述分析,可以认为,在疲劳载荷中,使位错钉扎的是由于溶质原子气团的形成。溶质原子在疲劳过程中通过空位的帮助进入位错,形成气团,使位错被钉扎。被钉扎的位错的动性减低,因而ΔE下降。在时效过程中,在位错线上成核的θ′和θ相,对于位错线也起着一定的钉扎作用。由上述的图象还可以推知,G.P.[1]区和G.P.[2]区不是在位错线上成核的,而θ′相和θ相则是在位错线上成核的。     

Evaluation of the mechanical properties of PMC interface using slice compression test — Analysis of transfer mechanism of interfacial shear stress

Properties of the fiber/matrix interface in SiO₂/epoxy and SiC/epoxy composite are investigated using the slice compression test (SCT) for the single fiber, where the specimen is loaded and unloaded between a plate which has different mechanical properties. It is found that the interfacial debonding proceeds from the polished surface at a soft plate side and that the fiber protrusion occurs after unloading. The fiber-protrusion length is directly measured at each applied stress level using a scanning electron microscope. Interfacial shear-sliding stress is obtained based on the constant shear-sliding stress analysis employing the obtained protrusion length. It is demonstrated that the value of interfacial shear-sliding stress shows good agreement with that obtained from another technique, the push-out test, on the same system. The relation between the fiber-protrusion length and applied stress is proportional to a certain extent. From this result, it is analytically pointed out that the applied stress has a limiting value in this SCT because of Poisson's effect. Also, two interfacial debonding criteria, which are determined analytically for the PMC, are discussed.