COD measurements at various positions along a crack

Load versus crack-opening displacement (COD) was measured at various positions along the border of a fatigue crack as it grew from a small surface crack on the edge of an aluminum specimen into a through-the-thickness crack. Displacements were measured with a laser-based interferometric system with a gage length of 70 m and a resolution of 0.01 m. These load-COD curves can be used to determine opening loads and thereby investigate the effect of closure on the growth of cracks. In general, the opening loads decrease as the crack grows. The compliances after the crack is fully open can also be measured, and show generally good agreement with the predictions of linear-elastic fracture mechanics.Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

Ductile–brittle transitions in the fracture of plastically-deforming,adhesively-bonded structures. Part I: Experimental studies

Rate effects for adhesively-bonded joints in steel sheets failing by mode-I fracture and plastic deformation were examined. Three types of test geometries were used to provide a range of crack velocities between 0.1 and 5000 mm/s: a DCB geometry under displacement control, a wedge geometry under displacement control, and a wedge geometry loaded under impact conditions. Two fracture modes were observed: quasi-static crack growth and dynamic crack growth. The quasi-static crack growth was associated with a toughened mode of failure; the dynamic crack growth was associated with a more brittle mode of failure. The experiments indicated that the fracture parameters for the quasi-static crack growth were rate independent, and that quasi-static crack growth could occur even at the highest crack velocities. Effects of rate appeared to be limited to the ease with which a transition to dynamic fracture could be triggered. This transition appeared to be stochastic in nature, it did not appear to be associated with the attainment of any critical value for crack velocity or loading rate. While the mode-I quasi-static fracture behavior appeared to be rate independent, an increase in the tendency for dynamic fracture to be triggered as the crack velocity increased did have the effect of decreasing the average energy dissipated during fracture at higher loading rates.     

Small-crack closure measurements in titanium alloys

An automated interferometric displacement gage was used to monitor crack-mouth-opening behavior of naturally initiated small surface cracks in a series of titanium alloys having a range of microstructures and deformation characteristics. Findings indicate that the transient development of crack closure plays a significant role in the early propagation of small fatigue cracks.Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 6–10.     

微小缺口/孔洞的激光衍射无损检测

基于裂纹和孔洞的小尺寸特征,提出了微小缺口/孔洞的激光衍射无损探测技术,给出了解析表达式.通过这一技术,对单向拉伸试件中所含单边缺口和中心孔洞在外载作用下的演化过程进行了实时原位检测,获得了缺口/孔洞孔径随载荷的变化曲线及模拟裂纹时裂纹的张开位移、裂纹开裂长度及应力强度因子等一系列断裂参数.     

Strip model plasticity analysis of mixed mode crack opening displacement in aluminum alloy LY12

Under mixed mode loading, the crack tip blunts and undergoes displacements in two directions, the normal and shear component corresponding to Mode I and Mode II loading, respectively. These local displacements are determined by the duplicated film method and used to analyze the behavior of mixed mode fracture in aluminum alloy LY12. The mixed mode resultant crack opening displacement (COD) at fracture initiation tends to increase more rapidly with increase of the Mode II shear component. The fracture initiation value of COD for pure Mode II loading is six (6) times greater than that for Mode 1 loading. The same applies to the maximum effective plastic strain crack growth near the crack front. Observed are two typical morphologies, the equal-axes dimples and the parabolic dimples with evidence of slippage as dominated, respectively, by Mode I and Mode II loading.     

Parameters controlling fracture resistance in functionally graded materials under mode I loading

In this investigation the fracture behavior of functionally graded materials (FGMs) was studied by means of experiments carried out on model polymer-based FGMs. Model graded materials were manufactured by selective ultraviolet irradiation of ECO [poly(ethylene carbon monoxide)], a photo-sensitive ductile copolymer that becomes more brittle and stiffer under exposure to ultraviolet light. The mechanical response of the graded material was characterized using uniaxial tensile tests. Single edge notched tension graded ECO specimens possessing different spatial variations of Young’s modulus, failure stress and failure strain were tested under remote opening loading. A full-field digital image correlation technique was used to measure in real-time the displacement field around the crack tip while it propagated through the graded material. The measured displacement field was then used to extract fracture parameters such as stress intensity factor and T-stress, and thus construct resistance curves for crack growth in the FGMs. For this loading configuration it was found that the nonsingular T-stress term in the asymptotic expansion for stresses needs to be accounted for in order to accurately measure the fracture resistance in FGMs. In addition, the influence of local failure properties (i.e., failure stress and failure strain) on crack growth resistance was investigated in detail. It was found that depending on the combined effects of the spatial variation of these two failure parameters, regardless of the spatial variation of the Young’s modulus, the FGM fracture resistance can either increase, decrease or remain constant with continued crack growth.     

Dynamic Fracture Properties of Titanium Alloys

Fatigue precracked specimens of three titanium alloys (6Al-4V, ELI, and Timetal 5111) were dynamically loaded in a drop weight tower system while the dynamic fracture toughness was inferred using Coherent Gradient Sensing, crack opening displacement, or strain gage methods. A comparison of the initiation toughness of the three materials as a function of loading rate and specimen thickness is made.     

On effects of thickness on ductile crack growth in mild steel

Critical crack opening displacement (COD) values have been examined for a range of specimen thicknesses. The COD at the initiation of fracture δ₁ is found to be constant, given a plane-strain crack-tip stress-state, whereas the COD at maximum load δ_max decreases with increasing thickness. The loads required to produce instability are found to vary with thickness, in a way analogous to behaviour observed under linear elastic conditions. Crack growth under constant load for a range of specimen thicknesses has been examined, and failure has been found to occur at loads below that associated with Δ_max,; the minimum load per unit thickness required to cause failure decreasing with specimen thickness.     

Measurements of crack growth in a solid at elevated temperature by holographic interferometry

Real-time holographic interferometry was used to follow the crack-opening displacement (COD) of a compact tension specimen of zirconium 2.5-percent niobium subjected to a constant tensile load at 120°C for a period of 860 h. This was made possible by a dimensionally stable invar plate placed beside the specimen as the reference for the alignment of holograms. A finite-element elasto-plastic stress-analysis code and measurements on a duplicate specimen with a clip gage were used to correlate the measured COD and the corresponding crack growth.     

Damage growth by debonding in a single fibre metal matrix composite: Elastoplasticity and strain energy density criterion

A displacement-based finite element-based numerical approach has been employed to study the damage growth in a unidirectional SiC/Al composite containing a pre-existing crack along the fibre/matrix interface. The composite is modeled as a two-material cylinder subjected to uniform displacement. A detailed analysis is made for the stress field in the vicinity of the debond crack tip. This approach incorporates an elastic-plastic analysis combined with a strain energy density criterion to predict debonded crack growth direction, extended stable growth and final termination. The influence of contact taking place between the debonded surfaces is also considered. It is shown that such surface contact leads to reduced stress and strain fields around the crack tip, while the extent of reduction is increased with debonding length. By combining the reduced stress field with the strain energy density criterion, a limiting value for the debonding extension can be calculated for the critical applied displacement that led to fibre fracture.     

An experimental method for determining dynamic fracture toughness

The boundary and loading conditions in many dynamic fracture test methods are frequently not well defined and, therefore, introduce a degree of uncertainty in the modeling of the experiment to extract the dynamic fracture resistance for a rapidly propagating crack. A new dynamic fracture test method is presented that overcomes many of these difficulties. In this test, a precracked, three-point bend specimen is loaded by a transmitter bar that is impacted by a striker bar fired from a gas gun. Different levels of energy can be imparted to the specimen by varying the speed and length of the striker to induce different crack growth rates in the material. The specimen is instrumented with a crack ladder gage, crack-opening displacement gage and strain gages to develop requisite data to determine toughness. Typical data for AISI 4340 steel specimen are presented. A simple quasi-dynamic analysis model for deducing the fracture toughness for a running crack from these data is presented, and the results are compared with independent measurements.     

Fatigue damage in centrally notched GR/EP laminates

The fatigue properties of graphite/epoxy (Gr/Ep) T300/5208 composite laminates of 16 plies with a central circular hole subjected to tension-tension (T-T) constant-stress amplitudes at room temperature and low humidity have been fully investigated. Studied are four types of notched laminates which are classified as unidirectional, off-axis, orthotropic shear and quasi-isotropic. Some of them were precracked to initiate and guide the crack growth transversely. Our work is experimental and the analysis is based on a semiempirical approach. We have experimentally measured S-N curves, failure surfaces, crack lengths and their corresponding growth directions, delamination areas and transverse delamination lengths for the above series of composites. The fatigue failure mechanism was observed and expressed schematically. To analyze the experimental results, we have categorized the S-N curves by three common equations. The effective transverse crack length of quasi-isotropic laminates was found to be independent of the applied stress. For simplicity, it was modeled by a power law of applied cycles. It was also found that the delamination area could be expressed by a power law of applied cycles. Hence, the so-called modified Paris law, i.e., the power law of cycles, proposed here has been verified as satisfactorily acceptable.     

A delamination gage for carbon fiber composites

A graphite crack gage familiar to fracture testing of nonconductive polymeric materials has been adapted to measure delamination growth in carbon fiber composites. The gage consists of a continuous graphite film whose conductance changes linearly with respect to crack length. The development of an insulation technique so that the electrical film may be applied to carbon fiber composites is described. Further constraints on the gage design occur due to the narrow profiles of conventional delamination specimens. These limitations are reviewed in detail along with appropriate methods for manufacturing and calibration of the gage for delamination experiments. A simple shunt voltage measurement circuit is described along with a derivation of the relationship of crack length to voltage. Two example applications are provided: stable delamination growth in a conventional double cantilever beam (DCB) specimen and dynamic delamination growth in a single-edge-notched (SEN) strip. The electrical delamination length measurements from the DCB tests were found to compare well with the location of the delamination front determined by microscopy and radiography. These results give confidence in dynamic delamination results where growth rates exceeding 1000 m/s were measured. Sample evaluations of delamination toughness are made using the experimental data; compliance methods are used in the case of the DCB analysis, and dynamic finite element methods are used in the case of the SEN strip analysis.     

Small attachable interferometric strain gages

Laser-based interferometry from two tiny reflective indentations can be used to measure in-plane strain/displacement over a very short gage length (on the order of 100 μm). If the specimen material is not reflective, then some other means of generating the interference patterns must be found. This paper describes two kinds of attachable gages: plated acetate replicas of indentations and reflective foils that are indented after application. In either case, the gage is applied with the techniques used for foil-resistance gages and the gage itself is very small. The manufacturing procedures are described. The results of experiments comparing the strain to that measured with foil-resistance gages are presented. Finally, the small interferometric gage is used to measure strain on one of the metal strips in a foil-resistance gage.     

EXPERIMENT STUDY OF I TYPE CRACK BLUNT EXTENSION INDUCED BY WEAK PLANE1)

天然裂缝或层理等弱界面的剪切破坏是体积压裂裂缝网络形成的关键因素。利用数字散斑相关技术,通过三点弯曲构建了I型裂缝经过弱界面时的扩展特性实验,获得了试件表面位移场和应变场的变化规律。实验结果表明：I型裂缝扩展至弱界面层后,裂缝发生短暂停滞扩展,裂缝尖端张开位移迅速增加,I型裂缝尖端钝化,弱界面剪切应变迅速增加,裂缝由I型裂缝转变为I-II复合型裂缝并转向扩展。     

混凝土复合型裂纹扩展的非局部近场动力学建模分析

基于非局部近场动力学理论,构建了修正的能反映混凝土宏观拉压异性和断裂特征的近场动力学本构模型,开发了相应的离散、加载和时间积分算法,实现典型混凝土构件中复合型裂纹扩展过程模拟。在物质点对尺度上定义局部损伤并考虑物质点对的相对转动,通过求解时空微-积分方程实现裂纹的自然萌生与扩展,避免裂尖不连续带来的求解奇异性、网格依赖性和网格重构以及常规近场动力学本构模型的泊松比限制。通过含单边和双边初始裂纹四点剪切混凝土梁裂纹扩展破坏全过程模拟,得到破坏形态、破坏荷载以及完整的荷载-裂纹开口滑移曲线,并与试验和其他数值模拟结果对比,验证了模型的精确性和算法的稳定性。     

Influence of the Matrix Type on the Mode I Fracture of Carbon-Epoxy Composites Under Dynamic Delamination

The delamination energy and fracture behaviour under static and dynamic mode I loading of two composites, made of the same unidirectional carbon reinforcement embedded in two different matrices, one tough and the other brittle, was investigated with the aim of analyzing the influence of the employed resin on the fatigue delamination behaviour of both composites. In the case of dynamic loading, the number of cycles necessary for the onset of delamination was determined for a given elastic energy release rate and crack growth rate for different critical energy rates. The double cantilever beam (DCB) test was found to be suitable for promoting the initial delamination. The experimental results confirm the enhanced performance of the tough resin both in terms of crack initiation and growth rate.     

Numerical simulation of fracture mode transition in ductile plates

Fracture mode of ductile solids can vary depending on the history of stress state the material experienced. For example, ductile plates under remote in-plane loading are often found to rupture in mode I or mixed mode I/III. The distinct crack patterns are observed in many different metals and alloys, but until now the underlying physical principles, though highly debated, remain unresolved. Here we show that the existing theories are not capable of capturing the mixed mode I/III due to a missing ingredient in the constitutive equations. We introduce an azimuthal dependent fracture envelope and illustrate that two competing fracture mechanisms, governed by the pressure and the Lode angle of the stress tensor, respectively, exist ahead of the crack tip. Using the continuum damage plasticity model, we demonstrate that the distinctive features of the two crack propagation modes in ductile plates can be reproduced using three dimensional finite element simulations. The magnitude of the tunneling effect and the apparent crack growth resistance are calculated and agree with experimental observations. The finite element mesh size dependences of the fracture mode and the apparent crack growth resistance are also investigated.     

Micro-mechanical modelling of fatigue damage in titanium metal matrix composites

In this work, the benefits from the blending between micro-structural fracture mechanics and elasto-plastic fracture mechanics in the analysis of fatigue damage in titanium metal matrix composites (TMCs) is presented. The efficiency of interfacial debonding and fibre bridging (FB) are shown not only to control crack growth but also to be responsible for severe crack growth changes taking place throughout the material's response under fatigue. A possible way to extract answers about the fatigue threshold, the operational life of the material and finally the fracture toughness is given in detail.