Multiple cracks identification for piezoelectric structures

We investigate through molecular dynamics simulations the fracture properties of boronitrene (BN), graphene, and their interfaces. Four types of interfaces between boronitrene and graphene are considered. It is found that the fracture toughness of graphene is highest among the examined models and is 3.61 and 4.24 \(\hbox {MPa}\sqrt{\hbox {m}}\) in the armchair and zigzag directions, respectively. Compared to graphene, boronitrene exhibits approximately 12 and 21% smaller values of the fracture toughness in the armchair and zigzag directions, respectively. In the armchair direction, the fracture toughness of the interface between boronitrene and graphene with B–C bonds in the interface is weakest and is about 2.49 \(\hbox {MPa}\sqrt{\hbox {m}}\), while the interfacial fracture toughness with C–N bonds in the interface is very close to that of graphene. In the zigzag direction, the interfacial fracture toughness is close to that of BN sheet. Under tension in the zigzag direction, a centered crack, which is initially perpendicular to the tensile direction, kinks at both tips in graphene and boronitrene regions. Since graphene has larger fracture toughness than that of boronitrene, an initial crack in their interface is forbidden to penetrate the graphene region; i.e., the crack can only propagate in the boronitrene region or along their interface of the hybrid BN/graphene sheets. The crack shape in the hybrid BN/graphene sheets depends on the arrangement of B–C–N atoms around the interface and the initial crack tip region.     

Fracture behaviour of 2D-weaved, silica–silica continuous fibre-reinforced, ceramic–matrix composites (CFCCs)

Significantly improved fracture resistance (in terms of fracture toughness and fracture energy) can be imparted to monolithic ceramics by adopting composite design methodology based on fibre reinforcement technology. The present paper describes the fracture behaviour of one such fibre-reinforced material, namely the silica–silica based continuous fibre-reinforced, ceramic–matrix composite (CFCC) in two orthogonal notch orientations of crack divider and crack arrester orientations. Different fracture resistance parameters have been evaluated to provide a quantitative treatment of the observed fracture behaviour. From this study, it has been concluded that the overall fracture resistance of the CFCC is best reflected by total fracture energy release rate (J_c), which parameter encompasses most of the fracture events/processes. The J_c values of the composite are found to be more than an order of magnitude higher than the energy values corresponding to the plane strain fracture toughness (J_KQ, derived from K_Ic, the plane strain fracture toughness) and >200% higher than elastic–plastic fracture toughness (J_Ic). Apart from this, the composite is found to exhibit high degree of anisotropy in the fracture resistance and also, a significant variation in the relative degree of shear component with crack extension.     

Effect of thickness on fracture criterion in general yielding fracture mechanics

In this research work, the effect of thickness on fracture criterion is studied for extra deep drawn (EDD) steel sheets. Experimental results are generated on fracture toughness of EDD steel sheets using compact tension specimens and a ‘maximum load’ as a fracture criterion. Critical crack tip opening displacement (CTOD) is found with the help of three methods: plastic hinge model (PHM), crack flank opening angle (CFOA) and finite element model (FEM). The fracture toughness is found to increase with increase in thickness of specimens. The fracture behaviour exhibited characteristics of general yielding fracture mechanics.     

Face/core interface fracture characterization of mixed mode bending sandwich specimens

Debonding of the core from the face sheets is a critical failure mode in sandwich structures. This paper presents an experimental study on face/core debond fracture of foam core sandwich specimens under a wide range of mixed mode loading conditions. Sandwich beams with E‐glass fibre face sheets and PVC H45, H100 and H250 foam core materials were evaluated. A methodology to perform precracking on fracture specimens in order to achieve a sharp and representative crack front is outlined. The mixed mode loading was controlled in the mixed mode bending (MMB) test rig by changing the loading application point (lever arm distance). Finite element analysis was performed to determine the mode‐mixity at the crack tip. The results showed that the face/core interface fracture toughness increased with increased mode II loading. Post failure analysis of the fractured specimens revealed that the crack path depends on the mode‐mixity at the crack tip, face sheet properties and core density.     

Impact of the anisotropy of fracture toughness on the propagation of planar 3D hydraulic fracture

Sedimentary rocks often exhibit a transverse isotropy due to fine scale layering. We investigate the effect of the anisotropy of fracture toughness on the propagation of a planar 3D hydraulic fracture perpendicular to the isotropy plane: a configuration commonly encountered in sedimentary basins. We extend a fully implicit level set scheme for the simulation of hydraulic fracture growth to the case of anisotropic fracture toughness. We derive an analytical solution for the propagation of an elliptical hydraulic fracture in the toughness dominated regime—a shape which results from a particular form of toughness anisotropy. The developed numerical solver closely matches this solution as well as classical benchmarks for hydraulic fracture growth with isotropic toughness. We then quantify numerically the transition between the viscosity dominated propagation regime at early time—where the fracture grows radially—to the toughness dominated regime at large time where the fracture reaches an elliptical shape in the case of an elliptical anisotropy. The time scale at which the fracture starts to deviate from the radial shape and gets more elongated in the direction of lower toughness is in accordance with the viscosity to toughness transition time-scale for a radial fracture defined with the largest value of fracture toughness. Similarly, the toughness dominated regime is fully reached along the whole fracture front when the time gets significantly larger than the same transition time-scale defined with the lowest value of toughness. Using different toughness anisotropy functions, we also illustrate how the details of the complete variation of fracture toughness with propagation direction governs the final hydraulic fracture shape at large time. Our results highlight toughness anisotropy as a possible hydraulic fracture height containment mechanism as well as the need for its careful characterization beyond measurements in the sole material axes (divider and arrester) directions.     

Effect of Layers Position on Fracture Toughness of Functionally Graded Steels in Crack Divider Configuration

In the present study, fracture toughness of functionally graded steels in crack divider configuration has been modeled. By utilizing plain carbon and austenitic stainless steels slices with various thicknesses and arrange- ments as electroslag remelting electrodes, functionally graded steels were produced. The fracture toughness of the functionally graded steels in crack divider configuration has been found to depend on the composites’ type together with the volume fraction and the position of the containing phases. According to the area under stress-strain curve of each layer in the functionally graded steels, a mathematical model has been presented for predicting fracture toughness of composites by using the rule of mixtures. The fracture toughness of each layer has been modified according to the position of that layer where for the edge layers, net plane stress condition was supposed and for the central layers, net plane strain condition was presumed. There is a good agreement between experimental results and those acquired from the analytical model.     

Fracture toughness of transverse cracks in graphite/epoxy laminates at cryogenic conditions

Stress singularity of a transverse crack normal to ply-interface in a composite laminate is investigated using analytical and finite element methods. Four-point bending tests were performed on single-notch bend specimens of graphite/epoxy laminates containing a transverse crack perpendicular to the ply-interface. The experimentally determined fracture loads were applied to the finite element model to estimate the fracture toughness. The procedures were repeated for specimens under cryogenic conditions. Although the fracture loads varied with specimen thickness, the critical stress intensity factor was constant for all the specimens indicating that the measured fracture toughness can be used to predict delamination initiation from transverse cracks. For a given crack length and laminate configuration, the fracture load at cryogenic temperature was significantly lower. The results indicate that fracture toughness does not change significantly at cryogenic temperatures, but the thermal stresses play a major role in fracture and initiation of delaminations from transverse cracks.     

Film cracking and debonding in a coated fiber

A fracture mechanics based methodology for the determination of interface fracture toughness from crack spacing in a thin coated fiber is presented. The coating (film) may be regarded as the matrix material in typical experiments employing this configuration. Matrix crack spacing is considered to be the result of a competitive process between matrix segmentation and interface debonding which are assumed to be governed by critical energy release rate criteria. Matrix cracks are assumed to form by the process of channeling in the circumferential direction and steady state conditions are assumed at the matrix crack front in the channeling direction. Energy release rates are determined using domain integral procedures in conjunction with the finite element method. The minimum crack spacing is obtained as a function of applied stress for different values of interface fracture toughness. A methodology to relate the saturated crack spacing to interface fracture toughness is developed. Interfaces are classified into three categories: weak, intermediate and strong. It is shown that in experiments of this type, quantitative information about the interface fracture toughness can be obtained for intermediate interfaces while qualitative information may be obtained for weak and strong interfaces.     

Dynamic fracture of a functionally gradient material having discrete property variation

A functionally gradient material (FGM) with discrete property variation is prepared, and the dynamic fracture in this material is studied using the technique of photoelasticity combined with high-speed photography. Transparent sheets required for the study are made by casting a polyester resin mixed with varying amounts of plasticizer. The mechanical (quasi-static and dynamic) and optical properties of the material are evaluated as a function of the plasticizer content. Results of material characterization show that the fracture toughness increases with increasing plasticizer content, whereas the Young's modulus decreases. The material fringe constant and the dynamic modulus are observed to be relatively insensitive to plasticizer content. The FGM is then prepared by casting together thin strips having different plasticizer content. The dynamic crack propagation phenomenon is studied for four different property variations along the crack propagation direction, and the effects of these property variations on crack speed, crack jump distance and dynamic stress intensity factor are investigated. Results of this investigation show that increasing the toughness in the direction of crack growth reduces the crack jump distance as compared to on increasing-decreasing toughness variation for the same initial energy.     

Interpreting the stress ratio effect on delamination growth in composite laminates using the concept of fatigue fracture toughness

This paper provides a study on fatigue delamination growth in composite laminates using energy principles. Experimental data has been obtained from fatigue tests conducted on Double Cantilever Beam (DCB) specimens at various stress ratios. A concept of fatigue fracture toughness is proposed to interpret the stress ratio effect in crack growth. The fatigue fracture toughness is demonstrated to be interface configuration independent but significantly stress ratio dependent. An explanation for this phenomenon is given using SEM fractography. Fracture surface roughness is observed to be similar in different interfaces at the same stress ratio. But it is obviously more rough for high stress ratio in comparison with that for low stress ratio, causing the fatigue resistance increase. Therefore, the stress ratio effect in fatigue crack growth can be physically explained by a difference in resistance to crack growth.     

Practical application of the weakest-link model to fracture toughness problems

This paper is intended as a first step towards the formalization of procedures for the application of the weakest-link model to fracture toughness problems. Loosely speaking, the weakestlink model states that the fracture toughness is determined by the most brittle region (“weakest link”) along the crack front. In practice, the model will often be applicable in some form if the mode of fracture is cleavage. It predicts that the distribution of fracture toughness is dependent on the length of the crack front. Methods are presented for the calculation of this crack-front-length effect. If there are no systematic fracture toughness variations along the crack front, and if the fracture mechanics parameter is constant along the crack front, it is rather simple to calculate; otherwise the calculations are somewhat more complicated.     

Fracture Toughness Characteristics of Stacked Bilayer Graphene via Far-Field Displacement Measurements

Mechanical properties of graphene, e.g., strength, modulus, and fracture toughness are extremely sensitive to flaws. Here the fracture properties of stacked bilayer graphene sheets (SBLG) are reported, obtained via stacking two individually grown graphene sheets. The SBLG is presented here as a building block for flaw-resilient nanomaterials. The fracture properties of freestanding SBLG sheets, suspended on transmission electron microscope (TEM) grids, are characterized by stretching the TEM grid inside an scanning electron microscope (SEM) chamber and monitoring the local displacements in real-time. The fracture toughness is measured and expressed as a function of the critical displacement required to propagate existing cracks in the experiment via computational models. This approach decouples force and displacements measurements, and utilizes the known elastic modulus along with the known displacement boundary conditions at the onset of crack growth to estimate the far field force and stress. This strategy represents a breakthrough in nanoscale fracture mechanics for statistical analysis and high throughput experimens on multiple samples at a time. Results demonstrate that the SBLG is markedly tougher than as-grown single or multilayer graphene, with a mode I fracture toughness of ≈28.06 ± 7.5 MPa$\sqrt{m}$. The mechanisms leading to a higher toughness of SBLG are also analyzed and discussed.     

Mode II Brittle Fracture Assessment Using ASFPB Specimen

The four-point bend specimen subjected to anti-symmetric loading (ASFPB) is frequently used for determining pure mode II fracture resistance of rock materials. It is shown in this paper that, when the applied loads are close to the crack plane, the ASFPB specimen does not provide pure mode II condition, since the effect of mode I also appears in crack tip deformation. A set of fracture test were also conducted on a type of marble using ASFPB configuration. The test results showed that fracture resistance is strongly dependent on the loading distance from the crack plane. The effective fracture toughness increases when the distance between the loading points and the crack plane decreases. It is shown that the enhanced fracture resistance of marble samples could be mainly because of very large negative T-stresses that exist for the mentioned loading situations.     

A finite element analysis of plane strain dynamic crack growth in materials displaying the Bauschinger effect

In this paper dynamic crack growth in an elastic-plastic material is analyzed under mode I plane strain small-scale yielding conditions using a finite element procedure. The main objective of this paper is to investigate the influence of anisotropic strain hardening on the material resistance to rapid crack growth. To this end, materials that obey an incremental plasticity theory with linear isotropic or kinematic hardening are considered. A detailed study of the near-tip stress and deformation fields is conducted for various crack speeds. The results demonstrate that kinematic hardening does not oppose the role of inertia in decreasing the plastic strains and stresses near the crack tip with increase in crack speed to the same extent as isotropic strain hardening. A ductile crack growth criterion based on the attainment of a critical crack opening displacement at a small micro-structural distance behind the tip is used to obtain the dependence of the theoretical dynamic fracture toughness with crack speed. It is found that for any given level of strain hardening, the dynamic fracture toughness displays a much more steep increase with crack speed over the quasi-static toughness for the kinematic hardening material as compared to the isotropic hardening case.     

Effects of deleterious impurities and cerium modificationon intrinsic and extrinsic toughening levels of AI-Li based alloys

Abstract

The toughness of AI-Li-Cu-Zr and AI-Li-Cu-Mg-Zr sheets containing various impurities and cerium concentrations, and AI-Li-Mg-Zr sheets containing various cerium concentrations under two aged conditions has been investigated by establishing the variabilities of intrinsic and extrinsic toughening levels and by determining the fracture toughness and the tensile ductility. The relationships of intrinsic and extrinsic toughening levels with fracture morphologies and microstructural parameters have been discussed. Iron and silicon impurities detract from the intrinsic toughening level although they do not have any important influence on the extrinsic toughening level. Sodium and potassium impurities significantly degrade the intrinsic toughening level although they may benefit the extrinsic toughening level to a certain degree. Cerium modification increases the intrinsic and extrinsic toughening levels of AI-Li-Cu-Zr alloy containing higher concentrations of iron and silicon impurities, resulting in an improvement of the fracture toughness. A small amount of cerium addition in Al-Li-Cu-Mg-Zr alloy rich in either Fe + Si or Na + K increases the intrinsic toughening level but decreases the extrinsic toughening level so that, overall, the fracture toughness is hardly affected. A certain amount of cerium addition in AI-Li-Cu-Mg-Zr alloy rich in iron and silicon improves the fracture toughness because both the intrinsic toughening level and the extrinsic toughening level are enhanced. However, for the AI-Li-Mg-Zr alloy, cerium modification does not bring about any improvement in the fracture toughness as the extrinsic toughening level is generally damaged. When impurities result in increased crack branching or when cerium addition promotes more marked lamellar type splitting, the extrinsic toughening level can usually be increased.     

Study of mode I crack dynamic propagation behaviour and rock dynamic fracture toughness by using SCT specimens

To study crack dynamic propagation behaviour and rock dynamic fracture toughness, a single cleavage triangle (SCT) specimen was proposed in this paper. By using these specimens and a drop‐weight test system, impact experiments were conducted, and the crack propagation velocity and the fracture time were measured by using crack propagation gauges. To examine the effectiveness of the SCT specimen and to predict the test results, finite difference numerical models were established by using AUTODYN code, and the simulation results showed that the crack propagation path agrees with the test results, and crack arrest phenomena could happen. Meanwhile, by using these numerical models, the crack dynamic propagation mechanism was investigated. Finite element code ABAQUS was applied in the calculation of crack dynamic stress intensity factors (SIFs) based on specimen dimension and the loading curves measured, and the curves of crack dynamic SIFs versus time were obtained. The fracture toughness (including initiation toughness and propagation toughness) was determined according to the fracture time and crack speeds measured by crack propagation gauges. The results show that the SCT specimen is applicable to the study of crack dynamic propagation behaviour and fracture toughness, and in the process of crack propagation, the propagation toughness decreases with crack propagation velocity, and the crack arrest phenomena could happen. The critical SIF of an arrest crack (or arrest toughness) was higher than the crack propagation toughness but was lower than the initiation toughness.     

A simplified method for measuring plane strain fracture toughness

A fracture toughness measuring concept is presented which is based on the use of specimen configurations for which the initial crack growth is stable under controlled force (“soft” machine) conditions. The concept is analyzed, and is demonstrated on a specimen configuration consisting of a short rod with narrow longitudinal slots for crack guides. Tests were conducted on two types of aluminum, PMMA, fused quartz and siltstone rock. It is shown that the fracture toughness test is very simple to perform, gives repeatable results, and is equally applicable to both ductile and brittle materials.     

混凝土断裂及亚临界扩展的细观机制

通过模型和三点弯曲断裂SEM试验,详细研究了混凝土断裂全过程及亚临界扩展的细观机理。结果表明:混凝土断裂是一个复杂的不规则过程,存在明显的亚临界扩展现象。混凝土亚临界扩展路径是曲折的,并非经典断裂力学假定的平直路径,混凝土亚临界扩展和临界失稳扩展呈现分形特征。用起裂断裂韧性iICK和分形等效断裂韧性feICK,来描述混凝土抵抗初裂和临界失稳扩展的能力。给出了考虑亚临界扩展弯折效应的混凝土亚临界扩展长度、混凝土起裂断裂韧性iICK和分形等效断裂韧性feICK,的计算表达式。计算表明:混凝土失稳断裂时的分形等效断裂韧性feICK ,与混凝土亚临界扩展的分维数D成正比。     

Influence of the thermomechanical processing on the fracture mechanisms of high strength aluminium/pure aluminium multilayer laminate materials

The microstructure and mechanical properties, with emphasis in the impact fracture toughness behaviour, of two multilayer laminate materials have been investigated. The multilayer materials are constituted by alternated sheets of pure aluminium (Al 1200 or Al 1050) and high strength Al 7075 alloy. Stacked layers of these alloys have been successfully joined using two processing routes with different total hot rolling strains. Both laminates have been tested at room temperature under impact Charpy tests, three-point bend tests and shear tests on the interfaces. Both laminates exhibited more than eight times improvement in impact fracture toughness over the monolithic Al 7075-T6. The toughness increase in the higher rolling strained laminate is almost entirely due to crack blunting mechanism, while in the lower strained laminate, crack deflection by delamination and crack renucleation processes were active.     

基于虚拟裂缝模型求解混凝土等效断裂韧度的实用解析方法

主裂缝亚临界扩展所形成的虚拟裂缝区的粘聚力是影响混凝土断裂韧度尺寸相关性的重要因素。根据混凝土准脆性材料的断裂特性,建立了一种基于虚拟裂缝模型的求解混凝土等效断裂韧度的实用解析方法。首先根据复合材料力学和线弹性断裂力学的基本原理,将虚拟裂缝的粘聚力作为相应的边界条件,运用修正的剪滞理论,分区引入变异层,建立了分层剪滞模型;然后根据能量法则,推导出求解混凝土等效断裂韧度的解析计算模式;最后针对相关试验的数值解,得到了混凝土等效断裂韧度的解析解。结果表明,对于不同的子层数,体积系列试件的混凝土等效断裂韧度均方差和变异系数分别低于0.0398和0.0384,高度系列试件的混凝土等效断裂韧度均方差和变异系数分别低于0.0394和0.0363,从而证明了混凝土等效断裂韧度是与试件尺寸无关的断裂参数;且与数值解相比,解析解的均方差和变异系数更小,证明了本文解析方法具有更好的鲁棒性。由此得出结论,基于虚拟裂缝模型所建立的解析模式为求解混凝土等效断裂韧度提供了一种可靠的、实用的解析方法。