Effect of crack face contact and friction on Brazilian disk specimens—A finite difference solution

A full curvilinear transformation is employed to study the effect of contact and friction on Brazilian disk specimens containing a crack and subjected to concentrated loads at angles 0° <  < 90°. Homogeneous and bimaterial disks made of glass and epoxy are considered. The effect of loading angle and friction coefficient on the stress intensity factors, as well as the contact length is studied. The results are compared to available semi-analytical and finite elements results. It is found that when the crack faces are in contact without stick zones, an increase in friction causes a decrease of the normal gap, tangential shift and stress intensity factors. When stick conditions appear in the contact zone, an increase in the coefficient of friction also results in increasing the stick zone within the contact zone.     

Brazilian disk test simulation intended for the study of interfacial cracks in bi-materials

The good mechanical characteristics of bimaterials and in particular those of the ceramic-metal couple would make them, industrially, an interesting alternative if their fracture behaviour was better understood. The difference of the mechanical properties of the bonded materials leads to a stress concentration at the vicinity of the interface. This study concerns the analysis of the interfacial fracture in Brazilian disk test, subjected to compressive load. The finite element method is used to carry out this objective. The study is limited to the case of an elastic behaviour of the two components of the assembly and to a pure junction. The behaviour of a crack located at the interface is analyzed by global approach based on the strain energy release rate. The difference of the mechanical properties of the two bonded materials leads to a mixed mode (mode I + II).     

Partially stiffened elastic half-plane with an edge crack

A technique, using the Brazilian disk specimen, for measuring the fracture toughness of unidirectional fiber-reinforced composites, over the entire range of crack-tip mode mixities, was developed. The fracture toughness of a graphite/epoxy fiber-reinforced composite was measured, under both mode-I and mode-II loading conditions. We found that for certain material orientations the mode-II fracture toughness is substantially higher than the mode-I toughness. The complete dependence of the fracture toughness on the crack-tip mixity was determined for particular material orientations and the phenomenological fracture toughness curves were constructed. Using the Brazilian disk specimen, together with a hydraulic testing machine, the fracture toughness of the composite under moderate loading rates was measured. We observed that the mode-I fracture toughness was not sensitive to the loading rate at the crack tip, K, while the mode-II ‘dynamic’ fracture toughness increased approximately 50 percent over the quasi-static fracture toughness. A qualitative explanation of the dependency of fracture toughness on crack-tip loading rate is discussed. Finally, a mechanical fracture criterion, at the microscopic level, which governs the crack initiation under mixed-mode loading conditions is presented; these theoretical predictions closely follow the trend of experimental measurements. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Calculation of the crack tip parameters in the holed‐cracked flattened Brazilian disk (HCFBD) specimens under wide range of mixed mode I/II loading

In this paper, the crack tip parameters including the stress intensity factors (K_I and K_II), T‐stress and the third terms of the stress field (A₃ and B₃) are determined comprehensively for a disk‐type sample named holed‐cracked flattened Brazilian disk (HCFBD) under various combinations of mode I and mode II loading. The HCFBD specimen is a circular disk containing a central hole in which the initial cracks are created radially from the hole circumference. Moreover, the ends of HCFBD are flattened for the sake of convenient loading. Performing enormous finite element analyses and calculating the stress intensity factors K_I and K_II, the states of pure mode II are determined for different configurations of HCFBD. Furthermore, the sign and magnitude of parameter A₃ which plays an important role to justify the geometry and size effects on the fracture toughness of quasi‐brittle materials are also determined for HCFBD with different geometrical ratios.     

A sandwich three-point bend specimen for testing mode-I interlaminar fracture toughness for fiber-reinforced composite materials

A sandwich three-point bend specimen has recently been proposed to test mode-I interlaminar fracture toughness for fiber-reinforced composite materials. The test composite consist of a thin layer bonded by two lateral reusable steel bars (Sohn et al. 1995). Some time earlier this specimen configuration was used to test fracture toughness of adhesives (Zdaniewsk et al. 1987). However, formulae for analysing its fracture mechanics parameters such as stress intensity factor and energy release rate can not be found in the literature. The lack of adequate formulae may explain why suitable quantitative analysis using this specimen configuration has not been achieved. In this paper, a simple and effective homogenisation method is used to change the bi-material system, which represents the specimen, into single uniform test material. This physical homogenisation is carried out by geometric change of the cross section of lateral steel parts based on equal deflection rigidity. For the transformed specimen configuration of single uniform material, the corresponding stress intensity factor solution from handbooks is available. Two formulae of stress intensity factor for the sandwich three-point bend specimen are given as upper limit and lower limit respectively, they are plotted with varying elastic tensile modulus mismatch. Then the relation between stress intensity factor and energy release rate, with special consideration of orthotropy of the tested composite material, is used to derive its energy release rate. The specimen and its formulae can also be applied to test other materials such as wood, welded joints (Burstow and Ainsworth, 1995), as well as to test dynamic fracture toughness. This revised version was published online in July 2006 with corrections to the Cover Date.     

50th Anniversary Article: Review on Interface Fracture and Delamination of Composites

In this review paper, a methodology for measuring the interface fracture toughness of a crack between two isotropic, homogeneous materials and a delamination between two laminae of unidirectional composite materials of differing directions is presented. Four cases are considered. Two isotropic material pairs are described: glass/epoxy and two ceramic clays. Similar studies are presented for two cross‐ply laminates: 0°/90° and +45°/?45. The Brazilian disk specimen was used to carry out mixed mode fracture tests. The load and crack or delamination length at fracture were measured and used in a finite element analysis to determine the displacement field. An interaction energy or M‐integral was used to obtain the stress intensity factors at failure. These in turn were employed to calculate the critical interface energy release rate and two phase angles ψ and φ, which measure the mode mixity. For the M‐integral and for each interface crack or delamination, the first term of the asymptotic solution of the fields is required. For two isotropic materials, these solutions are well known. For the laminates described here, they were determined by the Stroh and Lekhnittski formalisms. A failure criterion determined from first principles is presented. The values of , ψ and φ are used to specify the criterion for each material pair. A statistical analysis is presented, which predicts a 5% probability of failure.     

泡沫夹芯复合材料梁界面裂纹曲折扩展实验与数值模拟

采用双悬臂梁(DCB)试验研究了具有不同密度的PMI泡沫芯体的玻璃纤维增强复合材料夹芯梁界面裂纹曲折破坏路径。基于包含裂纹的物质点算法(MPM), 建立了与试验研究相适应的MPM模型, 在不同的面板/芯体模量比下计算了界面裂纹裂尖模态比和曲折破坏角, 并结合曲折破坏准则模拟了界面裂纹曲折破坏路径。数值模拟结果和试验现象吻合良好, 说明了本文中数值分析模型和方法的有效性。研究结果表明, 面板材料和芯体材料模量失配越严重, 界面裂纹发生曲折破坏时的破坏角越大; 裂纹折入芯体后, 在 Ⅰ 型为主的加载模式的支配下以基本平行于界面的方向扩展。      

On the use of Brazilian disc specimen for calculating mixed mode I-II fracture toughness of rock materials

The centrally cracked Brazilian disc specimen has been used frequently in the past for investigating mixed mode I-II fracture toughness in rock materials. However, a review of the available test results reveals that the conventional fracture criteria like the maximum tangential stress criterion always underestimate the mixed mode I-II fracture toughness data obtained from the Brazilian disc specimen. In this paper, a generalized maximum tangential stress criterion which takes into account the effects of the three fracture parameters K_I, K_II and T-stress is used for predicting the mixed mode fracture toughness data available in the literature for several types of rock materials tested with the Brazilian disc specimen. It is shown that the generalized maximum tangential stress criterion provides significantly improved predictions for the experimental results.     

Fracture analysis of facesheets in sandwich composites

There exist two fracture mechanisms in facesheets of sandwich composites consisting of the 0° and 90° plies, namely crack growth and crack blocking. The former is undesired since it may lead to failure of facesheets and even the core in sandwich composites. A shear-lag model is developed in this article and it gives a simple criterion governing these two mechanisms. It is established that, for a given ratio E_t/E_f of the elastic moduli in the transverse and fiber directions, there exists a critical facesheet thickness above which crack blocking is achieved and crack growth is prevented.     

Theoretical analysis of the effects of relative crack length and loading angle on the experimental results for cracked Brazilian disk testing

Based on the closed-form expressions of the stress intensity factors for a central cracked circular disk, four error transfer functions of the stress intensity factors were introduced in order to analyze the effect of the relative crack length and the error of loading angle on the experimental results for Brazilian disk testing. The analyzed results show that the precision of are relevant on the relative crack length and the error of loading angle. Further analysis show that the error of loading angle Δθ has a significant effect on the errors of under mixed-mode loading condition, but Δθ has nearly no effect on the error of K_I under pure mode I loading condition and smaller effect on that of K_II under pure mode II loading condition. Finally, the recommended range of the relative crack length is between 0.4 and 0.6.     

Fabrication and mechanical testing of glass fiber entangled sandwich beams: A comparison with honeycomb and foam sandwich beams

The aim of this paper is the fabrication and mechanical testing of entangled sandwich beam specimens and the comparison of their results with standard sandwich specimens with honeycomb and foam as core materials. The entangled sandwich specimens have glass fiber cores and glass woven fabric as skin materials. The tested glass fiber entangled sandwich beams possess low compressive and shear modulus as compared to honeycomb and foam sandwich beams of the same specifications. Although the entangled sandwich beams are heavier than the honeycomb and foam sandwich beams, the vibration tests show that the entangled sandwich beams possess higher damping ratios and low vibratory levels as compared to honeycomb and foam sandwich beams, making them suitable for vibro-acoustic applications where structural strength is of secondary importance, e.g., internal paneling of a helicopter.     

Fracture of a ductile layer constrained by stiff substrates

A combined experimental and theoretical analysis of the fracture behaviour of brass/solder/brass sandwich specimens is conducted. First, the theories of interfacial fracture initiation for a ductile layer sandwiched between elastic substrates are reviewed. The fracture behaviours are then reported of brass/solder/brass sandwich specimens under various mode mixities. Additionally, the effects of solder layer thickness h and specimen lateral thickness t are presented. The effects of mode mix and plastic constraint on the failure mechanism and toughness are analysed.     

橡胶夹层/复合材料粘接界面疲劳裂纹扩展行为的研究

用 型加载下的双悬臂夹层梁试样 ,以应变能释放率为裂纹扩展参量 ,研究橡胶夹层 /复合材料粘接界面疲劳裂纹的扩展行为。结果表明 ,循环载荷下的裂纹扩展速率对试验频率、载荷比、温度及橡胶夹层厚度反映较敏感。     

缝纫泡沫夹芯复合材料细观纤维柱破坏行为

缝纫泡沫夹芯复合材料中的纤维柱在拔出过程中的破坏行为复杂导致结构承载性能难以预测。采用真空辅助树脂注射(VARI)工艺制备了缝纫泡沫夹芯复合材料,并使用层间拉伸试验(ITT)研究了缝纫泡沫夹芯复合材料中含有单根缝线纤维柱细观试件的破坏过程。讨论了不同破坏现象对缝线纤维柱拔出摩擦过程的影响,并分析了缝纫泡沫夹芯复合材料的破坏模式。分析了缝线粗细的变化对试件破坏过程中关键的力、位移等参数及能量吸收性能的影响。研究了由于成型工艺所导致的缺胶现象对缝纫泡沫夹芯复合材料性能的影响。结果表明:缝纫泡沫夹芯复合材料的能量吸收性能、关键位移参数及最大载荷都随着缝线变粗而增大。但是缝纫泡沫夹芯复合材料的破坏模式对其也有一定的影响,导致了变化趋势的波动;缺胶缝纫泡沫夹芯复合材料由于缺陷的存在,最大破坏载荷和能量吸收性能均有所下降。     

Cohesive layer models for predicting delamination growth and crack kinking in sandwich structures

There are potentially two types of fracture that sandwich structures with strong and stiff facing sheets and lightweight cores are liable to suffer. These are the delamination growth at the face-sheet core interface and crack kinking into the sandwich core, respectively. The paper proposes computational models to simulate these failure mechanisms. The models employ the cohesive layer concept and are so constructed as to ensure that the crack advance is controlled by the critical value of strain energy release rate in mode I fracture. Of these, the first model can treat only delamination along a predetermined plane and is designated as CLD (cohesive layer delamination model). The performance of this model is thoroughly investigated in the light of experimental results. The influence of the key parameters of the model, viz. the thickness of the cohesive layer and the strength and stiffness of the cohesive layer material, have been studied. It is found that the model, as developed in this study, is fairly robust and is not sensitive to changes in parameters other than the critical strain energy release rate. The second model can track crack growth which is not predetermined in its direction. This it does by identifying the element in which the maximum principal tensile stress exceeds a critical value; once a crack is nucleated, the stress across the crack is relieved so that the right amount of energy is released when the crack is fully developed - much in the same manner as in a cohesive layer model. This model is designated as CLDK (Cohesive Layer Delamination and Kinking) model as it deals with interfacial delamination and crack kinking- whichever is the preferred mode of fracture. Experimental results of three sandwich specimens, viz. bottom restrained beams with 0° and –10° tilt angle, respectively, and a compressed beam, were used for comparison. The results indicate that the both the models are able to capture the initiation and track the growth of the interfacial delamination. The CLDK model is capable in addition to track the crack kinking into the core, and its subsequent return to the face sheet-core interface.     

Effect of plastic anisotropy of weld on limit load of undermatched middle cracked tension specimens

Plastic anisotropy may have a significant effect on the limit load of structures. The present paper shows its effect on the limit load of well‐undermatched middle cracked tension specimens assuming that the base material is elastic and the weld material obeys Hill's quadratic orthotropic yield criterion in rigid‐perfect plasticity. The solution is based on a kinematically admissible velocity field, which is compatible with a stress field satisfying the equilibrium equations and the yield criterion in the plastic zone. The velocity field is singular in the vicinity of the bi‐material interface, which is typical for isotropic materials.     

Numerical investigation of creep crack growth in cross‐weld CT specimens. Part II: influence of specimen size

A numerical investigation of the influence of specimen size on creep crack growth in cross‐weld CT specimens with material properties of 2.25Cr1Mo at 550 °C is performed. A three‐dimensional large strain and large displacement finite element study is carried out, where the material properties and specimen size are varied under constant load for a total of eight different configurations. The load level is chosen such that the stress intensity factor becomes 20 MPa √m regardless of specimen size. The creep crack growth rate is calculated using a creep ductility‐based damage model, in which the creep strain rate ahead of the crack tip perpendicular to the crack plane is integrated taking the degree of constraint into account. Although the constraint ahead of the crack tip is higher for the larger specimens, the results show that the creep crack growth (CCG) rate is higher for the smaller specimens than for the larger ones. This is due to much higher creep strain rates ahead of the crack tip for the smaller specimens. If, on the other hand, the CCG rate is evaluated under a constant C * condition, the creep crack growth rate is found to be higher for the larger specimens, except when the crack is located in a HAZ embedded in a material with a lower minimum creep strain rate; then, the creep crack growth rate is predicted to be higher for the smaller specimen. In view of these results, it is obvious that the size effect needs to be considered in assessments of defected welded components using results from CCG testing of cross‐weld CT specimens.     

含半椭圆表面裂纹焊接接头断裂参量的试验研究

本文研究了半椭圆形表面裂纹最深点三维J积分的直接测试技术,并在此基础上,通过对高匹配焊接接头表面裂纹试样断裂力学参量J积分的试验测试,探讨了接头强度匹配对焊接表面裂纹扩展驱动力的影响。试验表明本文所采用的手段对于焊接表面裂纹断裂参量的测试是适用的,且结果也充分反映出焊接接头的力学性能不均匀性的影响作用。     

双向荷载作用下空间夹心节点受力性能试验研究

节点核心区采用同梁等强的低强度混凝土浇筑的夹心节点和采用同柱等强的高强度混凝土浇筑的传统节点相比,施工简单且易保证质量,但是我国规范对其规定过于简单,没有明确的验算方法。通过三组不同混凝土强度等级差的空间夹心节点和传统节点对比试件的双向低周往复性能试验研究,对比分析了二者破坏形式、延性、耗能、变形和承载力等方面的差异,结果表明:中低剪压比夹心节点的整体抗震性能稍弱于传统节点,但相差不明显;中低轴压比、剪压比条件下,当柱与梁混凝土强度等级之比小于1.5时,节点区可直接采用与梁相同强度等级的混凝土浇筑,当柱与梁混凝土强度等级之比大于1.5时,其破坏形式可转变为节点核心区剪切破坏,需采取相应的加强措施。最后在此基础上,给出了与试验结果吻合较好的夹心节点抗剪承载力计算公式。