Mixed-mode crack growth in plates under three-point bending

A combined theoretical and experimental study of the problem of crack growth in a plate subjected to unsymmetrical three-point bending was undertaken. The opening-modeK _I and sliding-modeK _II stress-intensity factors describing the local stress field around the crack tip were determined by a finite-element computer program. The crack growth was analyzed by the maximum circumferential stress and the minimum strain-energy density criteria. The critical loads for crack growth and the crack trajectories were determined both by theory and experiment. The experimental results corroborated the theoretical predictions.     

Some transient coupled thermoelastic crack problems

This paper is concerned with determining the elastodynamic response of a plane strain medium containing a central crack deformed by the action of suddenly applied thermal and/or mechanical disturbances when the assumptions of the general theory of coupled thermoelasticity are assumed. Integral transform solution is employed to reduce the governing equations into integral equations of Fredholm type. A numerical inversion technique is used to compute the dynamic stress-intensity factors when the faces of the crack are subjected to constant heat flux and/or mechanical loading. Attention is focused on the overshoot in the stress-intensity factor and its time interval for non-stationary temperature fields, and to what degree it is influenced by the mutual dependence of the temperature and displacement fields inherent in the coupled theory of thermoelasticity.     

Determination of fracture toughness by photoelastic coating

The photoelastic-coating method was applied to the determination of fracture toughness in aluminum plates. The specimens were plates with a central transverse crack. Determinations were made first by the compliance method. The specimens were loaded statically to failure. The opening displacement across the crack was measured with a clip gage. In using this photoelastic-coating method, the stress-intensity factor was obtained in terms of the radius and fringe order of various isochromatic fringe loops using an extrapolation law. An apparent stress-intensity factor was obtained from several isochromatic fringe patterns away from the crack tip and then extrapolated to the crack tip to determine the true value. Results obtained by the photoelastic-coating method are higher than those obtained by the compliance method for all loads, due to the bluntness of the crack tip in the first set of specimens. Theoretical predictions fall between the compliance method and photoelastic-coating results. Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

用光弹性法测定复合应力强度因子

工程结构裂纹尖端应力强度因子(SIF)由于形状、荷载的复杂性及边界条件的不确定性,难以用解析法得到,数值计算也有困难,而光弹性法弥补了上述方法的不足。本文用环氧树脂制作圆轴模型,采用机加工的方法制作圆轴模型裂纹,然后将加载模型进行应力冻结,通过光弹性实验研究分析了圆轴裂纹尖端应力分布。由于带环形裂纹的圆轴在弯扭组合变形时,离中性轴最远的裂纹尖端处于复合裂纹状态,而三维光弹性应力冻结法是测定复杂三维问题复合裂纹的有效方法。本文用双参数法测定I型应力强度因子,用切片逐次削去法测定Ⅲ型应力强度因子,实验误差较小。     

Crack propagation in glass coatings under expanding spherical contact

The growth of transverse cracks under expanding spherical contact in a model system consisted of soda-lime glass bonded to a polycarbonate substrate is observed in situ from below or from the polished edge of the bilayer. Abrasion or chemical etching is employed on the coating surfaces to control the initial fracture. In the limit case of monoliths, the crack mouth becomes fully engulfed by the expanding contact, which results in a much steeper crack angle compared to the classical Hertzian cone case. As the coating thickness is reduced, flexure stresses are set in the coating which drive the cone crack to well away from the contact circle and initiate semi-elliptical-like radial cracks at the subsurface, right under the contact. Common to all three fracture modes is an initial unstable propagation phase following by a stable growth, with detrimental failure associated with severe damage to the top surface and/or delamination at the coating/substrate interface taking place at loads several times the fracture initiation loads.LEFM in conjunction with a large-strain FEM contact code is used to study the post-initiation fracture, with the crack path controlled by the principal stress trajectory or zero-mode II S.I.F. The analysis exposes the leading geometric and material parameters in each fracture mode, which may be useful in the design of bilayer structures for optimal mechanical performance. The well-known Auerbach law governing the initial fracture of monoliths is found to apply also to the bilayer crack systems within a certain range of the problem parameters. The numerical prediction for the crack profiles and the fracture envelopes generally collaborate well with the tests.     

Impact of thermal loads on interfacial debonding in FRP strengthened beams

The effect of thermal loads on the debonding mechanisms in beams strengthened with externally bonded composite materials is analytically investigated. The analytical approach adopts a high-order stress analysis model and a fracture mechanics model that uses the concept of the energy release rate through the thermo-mechanical form of the J-integral. The two models are combined to synthesize the relation between the energy release rate, the mechanical loads, the thermal loads, and the interfacial crack length simulating the thermo-mechanical debonding process. The model is supported through comparison with experimental results taken from the literature. The comparison quantifies and explains various phenomena observed in the experiments and mainly the non-monotonic dependency of the debonding failure load on the temperature. The impact of the temperature on the interfacial stresses and on the stability of the debonding process is also studied. Finally, the effect of an uniform thermal load on the debonding behavior of a strengthened beam is studied revealing the impact of the thermal load on the debonding stability and strength characteristics.     

Temperature distributions and thermal stresses in a partially filled annulus

The problem consists of determining the temperature distribution and the thermal stresses in an annulus partly filled with a cold fluid with free convection in air as the outer thermal-boundary condition. An iterative computer solution provided temperature distributions which were compared to those measured experimentally. Analytical calculations of the stresses using Fourier series expression for the temperature distribution agreed with experimental results by photothermoelasticity. The stress-intensity factors determined by photothermoelasticity for partly filled annuli with a crack extending radially 1/5 of the wall thickness were compared with approximate analytical methods.     

Residual fracture energy of cement paste, mortar and concrete subject to high temperature

Quantifying high temperature damage is an issue that can hardly be dealt with experimentally because of the complexity of the loading control, of temperature and of moisture. The experimental investigation was carried out. The measurement of the mechanical characteristics (fracture energy, tensile strength, elastic modulus and thermal damage parameter) of five cementitious materials, cement paste, mortar, ordinary concrete and two HPC concretes were performed by three-point bending tests after heating/cooling cycles at 120, 250 and 400 °C. The tests showed that the cementitious materials behave almost identical when the fracture energy G_f is considered as a function of maximum temperature. The thermal damage due to heating from 120 to 400 °C increases the fracture energy by 50% with the reference tests at room temperature. A more tortuous crack surface is one reasonable explanation for the significant increase in G_f. It is demonstrated that the temperature exposure makes all cementitious materials tested significantly more ductile and less resistant.     

Stress-intensity factors for surface cracks in functionally graded materials under mode-I thermomechanical loading

This paper describes the development and application of a general domain integral method to obtain J-values along crack fronts in three-dimensional configurations of isotropic, functionally graded materials (FGMs). The present work considers mode-I, linear-elastic response of cracked specimens subjected to thermomechanical loading, although the domain integral formulation accommodates elastic–plastic behavior in FGMs. Finite element solutions and domain integral J-values for a two-dimensional edge crack show good agreement with available analytical solutions for both tension loading and temperature gradients. A displacement correlation technique provides pointwise stress-intensity values along semi-elliptical surface cracks in FGMs for comparison with values derived from the proposed domain integral. Numerical implementation and mesh refinement issues to maintain path independent J-values are explored. The paper concludes with a parametric study that provides a set of stress-intensity factors for semi-elliptical surface cracks covering a practical range of crack sizes, aspect ratios and material property gradations under tension, bending and spatially-varying temperature loads.     

A moving-load controlled-displacement fracture-toughness testing machine

In conventional fracture-toughness testing, the line of application of the loads remains fixed with respect to specimen geometry. In this testing machine, the load moves with the advancing crack front, and displacement is used as the controlled variable to propagate and arrest a crack. The energy-release rate at the onset of crack propagation and, hence, the plane-strain fracture toughnessK _Ic can be measured directly without compliance calibration or stress-intensity evaluation. The specimen is in the form of a flat plat 25 by 50 cm which is simple to machine and provides about 30 values ofK _Ic. The versatility of the machine is demonstrated by making a statistical analysis ofK _Ic for 7075-T6 Al by showing the effect of plate thickness on the fracture toughnessK _c using a tapered specimen, and by evaluatingK _c in 7075 Al as a function of aging temperature in a thermal-gradient-treated specimen.     

A hybrid model for computationally efficient fatigue fracture simulations at microelectronic assembly interfaces

Modern microelectronic assemblies are heterogeneous, layered structures joined by interconnects made of solder alloys with low homologous temperatures. The solder interconnections join devices to circuit boards and they fail by thermal fatigue fracture at their interfaces either to the device or to the circuit board. Predicting the fatigue fracture of the solder interconnections is a challenge due to the fact that they undergo large inelastic deformations during temperature cycling tests. In this paper we develop a hybrid approach inspired by cohesive zone fracture mechanics and the Disturbed State Concept to predict the crack trajectory and fatigue life of a solder interconnection subjected to both isothermal temperature cycling and anisothermal temperature cycling conditions (representing the two common accelerated test conditions for microelectronic products). A hybrid computational approach is used in which a first order approximation of the disturbance is used to estimate incremental cycles to criticality and thereby propagate the crack. The modeled crack fronts and the fatigue lives are validated through a comparison to results from the two types of accelerated tests. Overall, the model is shown to predict the fatigue life of the critical interconnection in the assembly to within 20% of the experimentally determined life. More importantly, the predicted crack trajectory is demonstrated to agree very well with the experimentally observed trajectory. Strikingly, the microscopically observed microstructural changes during crack propagation from that corresponding to creep fatigue to that of shear overload were found to be excellently correlated with the rate of change of the disturbance calculated in the model.     

Transient thermal fracture of cracked plates

The effects of a transient thermal load on a cracked plate are studied experimentally using photothermoelasticity. The three crack configurations of an edge crack, an interior vertical crack and an interior crack inclined at 45 deg are analyzed. In each case, the initially heated plates are subjected to cooling along the edge, while the faces of the plate are either completely insulated, or noninsulated, or in a third case, they are covered with heated transparent Plexiglas plates. It is shown that among the three cracks, the largest transient maximum stress-intensity factor occurs for the edge crack. The inclined crack is subjected to a mixed-mode loading. Among the three cooling conditions, the most severe is the insulated faces case while the noninsulated is the least severe. The relative effect of the cooling conditions on the stress-intensity factors for the three crack types is different enough that the results with one cooling condition would not represent those of another one. A comparison of the experimental transient stress-intensity factors for the vertical crack cases to the finite-element results shows good agreement.     

利用维氏和玻氏压头表征半导体材料断裂韧性

压痕法是测量材料断裂韧性 ($K_{\rm IC})$ 的常用方法之一, 如何根据不同的材料、不同的压头选择适合的公式, 是当前面临的一大问题. 因此,在不同载荷下对单晶硅 (111) 和碳化硅 (4H-SiC, 0001面) 这两种半导体材料进行了维氏微米硬度和玻氏纳米压痕实验, 对实验产生的裂纹长度$c$进行了统计分析, 并采用13个压痕公式计算材料的$K_{\rm IC}$, 开展了微米划痕实验, 验证压痕法评估半导体材料$K_{\rm IC}$的适用性. 研究结果表明: 为了消除维氏压痕实验产生的$c$的固有离散性, 需要多次测量取平均值; 裂纹长度与压痕尺寸的比值随压痕载荷的增大而增大; 材料的裂纹类型与载荷相关且低载荷下表现为巴氏裂纹, 高载荷下表现为中位裂纹; 与微米划痕实验得到的单晶硅和碳化硅材料的$K_{\rm IC}$平均值 (分别为0.96 MPa,$\cdot$,$\sqrt{\rm m}$和2.89 MPa,$\cdot$,$\sqrt{\rm m}$) 相比, 在同一压头下无法从13个公式中获得同时适用于单晶硅和碳化硅材料的压痕公式,但在同一材料下可以获得同时适用于维氏和玻氏压头的$K_{\rm IC}$计算公式; 基于中位裂纹系统发展而来的压痕公式更适合用于评估半导体材料的$K_{\rm IC}$, 且维氏压头下的$K_{\rm IC}$与玻氏压头下$K_{\rm IC}$的关系不是理论上的1.073倍, 应为1.13$\pm 压痕法是测量材料断裂韧性(K_(IC))的常用方法之一,如何根据不同的材料、不同的压头选择适合的公式,是当前面临的一大问题.因此,在不同载荷下对单晶硅(111)和碳化硅(4H-Si C, 0001面)这两种半导体材料进行了维氏微米硬度和玻氏纳米压痕实验,对实验产生的裂纹长度c进行了统计分析,并采用13个压痕公式计算材料的K_(IC),开展了微米划痕实验,验证压痕法评估半导体材料K_(IC)的适用性.研究结果表明:为了消除维氏压痕实验产生的c的固有离散性,需要多次测量取平均值;裂纹长度与压痕尺寸的比值随压痕载荷的增大而增大;材料的裂纹类型与载荷相关且低载荷下表现为巴氏裂纹,高载荷下表现为中位裂纹;与微米划痕实验得到的单晶硅和碳化硅材料的K_(IC)平均值(分别为0.96 MPa·m~(1/2)和2.89 MPa·m~(1/2))相比,在同一压头下无法从13个公式中获得同时适用于单晶硅和碳化硅材料的压痕公式,但在同一材料下可以获得同时适用于维氏和玻氏压头的K_(IC)计算公式;基于中位裂纹系统发展而来的压痕公式更适合用于评估半导体材料的K_(IC),且维氏压头下的K_(IC)与玻氏压头下K_(IC)的关系不是理论上的1.073倍,应为1.13±0.01.     

基于统一相场理论的早龄期混凝土化-热-力多场耦合裂缝模拟与抗裂性能预测

受水化反应和热量传输等过程影响, 混凝土在养护阶段会发生受约束收缩变形, 并由此在结构内引发较大的拉应力, 而此时混凝土力学性能往往还处于较低水平, 容易导致建造期混凝土结构即出现裂缝等病害. 这种早龄期混凝土裂缝对核安全壳、桥梁隧道、地下结构、水工或海工结构等重大土木工程和基础设施的全生命周期完整性、耐久性和安全性造成严重影响. 为了准确预测早龄期混凝土抗裂性能并量化裂缝演化对混凝土结构行为的不利影响, 亟需开展化-热-力多场耦合环境下的混凝土裂缝建模与抗裂性能分析研究. 针对这一需求, 本工作在前期提出的固体结构损伤破坏统一相场理论基础上, 考虑开裂过程与水化反应、热量传输等之间的相互影响, 建立裂缝相场演化特征(包括基于强度的裂缝起裂准则、基于能量的裂缝扩展准则和基于变分原理的扩展方向判据等)与混凝土水化度和温度之间的定量联系, 提出混凝土化-热-力多场耦合相场内聚裂缝模型, 发展相应的多场有限元数值实现算法并应用于若干验证算例. 数值模拟结果表明, 上述多场耦合相场内聚裂缝模型合理地考虑了水化反应、热量传输、力学行为以及裂缝演化之间的耦合效应, 揭示了早龄期混凝土热膨胀变形和自收缩变形的相互竞争机理, 且分析结果不受裂缝尺度和网格大小等数值参数的影响, 实现了早龄期裂缝演化全过程准确模拟和抗裂性能定量预测, 有望在混凝土结构早龄期裂缝预测和控制方面发挥重要作用.      

Stress-intensity distributions for corner cracks emanating from open holes in plates of finite width

A series of frozen stress photoelastic tests is carried out in the present investigation. Linear Elastic Fracture Mechanics is used to analyze the problem of a part-through corner crack at an open hole in a plate of finite width loaded in tension. The photoelastic modeling capability of three-dimensional subcritical crack growth problems is assessed. This is achieved by comparing monotonically grown flaw shapes in epoxy models with crack profiles relative to fatigue crack propagation tests in a different material. Photoelastic stress-intensity factor distributions are checked against numerical results obtained for quarter elliptical geometries. The dependence of stress intensity factors on flaw shape is also discussed.     

Determination of mixed-mode stress-intensity factors K I and K II for a subsurface crack near a concentrated force

Two-dimensional photoelastic experiments were conducted to obtain isochromatic fringe fields in the region between a crack tip and a concentrated load on the boundary of a half plane. An analysis method is developed to determine the mixed-mode stress-intensity factors due to two interacting stress singularities. The results obtained showed the dominance of the opening mode in extending a delamination crack by sliding surface loads. Paper was presented at the 1989 SEM Spring Conference on Experimental Mechanics held in Cambridge, MA on May 28–June 1.     

Interfacial transient thermal fracture of adhesively bonded dissimilar materials

The effect of a transient thermal load on an interface crack in adhesively bonded dissimilar materials was experimentally studied by using photothermoelasticity. It is determined that the effect of the thermal load is to cause mostly shearing deformations at the crack tip. For two configurations, a horizontal crack (normal to the heat flow direction) and a vertical crack (parallel to the heat flow direction), it is shown that increasing the adhesive thickness results in steady-state and maximum transient strain-energy release rates and stress-intensity factors of smaller magnitudes. It is also found that the ratio of mode I to mode II stressintensity factors for the vertical crack is larger than the one for the horizontal crack.     

Crack propagation in layered plates—an experimental study

The effects of the layer height and the material properties of a layered medium on the propagation mode of a crack are discussed. Crack-propagation velocities and dynamic stress-intensity factors were evaluated during fracture and the corresponding curves were plotted. The medium consisted of two identical external layers and a middle layer of softer or harder material. This layer contained an initial crack which ran parallel to the interfaces of the layers. All phases of the specimens were fabricated from epoxy polymers. After the preparation of the middle layer, the surrounding layers were successively cast along the middle layer's straight boundaries without applying any kind of adhesive. High-speed photography and dynamic caustics were utilized to establish the changes in crack speeds and intensities of the stress field. The influence of geometry and especially of the height of the middle layer and the mechanical properties of the layered material was studied; interesting results were derived.     

Variation in stress-intensity factor and back-surface displacement for surface cracks

Knowledge of the magnitude and variation in the stress-intensity factor (SIF) around the perimeter of a surface crack is essential for an accurate analysis of a flawed component. SIFs for surface flaws of various semi-elliptical geometries were analytically determined. Three-dimensional linear-elastic finite-element analysis was performed to determine the maximum SIF for bending and tension for each of 12 crack geometries which represent deep surface flaws in finite-thickness plates. Experimental verification of one of the crack geometries was performed. Interferometry techniques were used to determine the actual variation in SIF along the curve crack front due to bending. In addition to the SIF calculations, physical characteristics are noted as observed in the analytical and experimental evaluations.     

Determination of fracture parameters using embedded fiber-optic sensors

The applicability of embedded fiber-optic sensors for the determination of fracture parameters is demonstrated. A Mach-Zehnder interferometric setup is used and mode-1 stress-intensity factors are obtained by embedding single-mode fibers in single-edge-notched specimens fabricated from Plexiglas. Optical fibers are embedded in-plane to measure axial strains at various depths and also in the transverse direction to measure the transverse strains, from which stress-intensity factors are determined. In both cases the experimental results compare well with the theoretical predictions.