Crack-tip dynamic isochromatics in the presence of small-scale yielding

A plasticity correction factor for the dynamic stress-intensity factor,K _I ^dyn , associated with a propagating crack tip in the presence of small-scale yielding, is derived from Kanninen's solution for a constant-velocity Yoffe crack with a Dugdale-strip yield zone. Distortions in the otherwise elastic isochromatics surrounding the constant-velocity crack tip are also studied by the use of this model. This plasticity correction factor is then used to evaluateK _I ^dyn from the dynamic isochromatics of a propagating crack in a 3.2-mm-thick polycarbonate wedge-loaded rectangular double-cantilever-beam specimen. The correctedK _I ^dyn is in good agreement with the corresponding values computed by a dynamic, elastic-plastic finite-element code executed in its generation mode.     

A bar impact tester for dynamic fracture testing of ceramics and ceramic composites

A bar impact test was developed to study the dynamic fracture responses of precracked ceramic bars, Al₂O₃ and 15/29-percent volume SiC_w/Al₂O₃. Crack-opening displacement was measured with a laser-interferometric displacement gage and was used to determine the crack velocity and the dynamic stress-intensity factorK _I ^dyn . The crack velocity andK _I ^dyn increased with increasing impact velocity while the dynamic-initiation fracture toughness,K _Id, did not vary consistently with increasing impact velocities.Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas on June 8–11.     

Unsteady Dynamic Crack Propagation in a Brittle Polymer

Dynamic crack propagation in a brittle polymer, poly(methyl-methacrylate) (PMMA), was studied using the method of caustics in combination with a Cranz–Schardin high-speed camera. Four different types of specimen geometry and loading method were employed to achieve the crack acceleration, deceleration, and/or reacceleration processes in one fracture event. The dynamic stress intensity factor K _ID and crack velocity were obtained in the course of the crack propagation and the corresponding relationship was determined. The effect of the crack acceleration and deceleration on the K _ID-velocity relationships was as follows: (1) the variations of K _ID and the velocity were strongly influenced by the specimen geometry and loading method; (2) the velocity change was qualitatively in accord with K _ID; (3) K _ID for a constant crack velocity was larger when the crack decelerated than it was when the crack accelerated or reaccelerated; (4) K _ID for an acceleration-free crack was uniquely related to the velocity; and (5) K _ID could be expressed as two parametric functions of the velocity and acceleration.     

Stress intensity factor range and propagation mode of surface cracks under rolling–sliding contact

Finite element analyses were conducted in order to evaluate the mode I and mode II stress intensity factors for inclined edge cracks under cyclic contact load under rolling and rolling–sliding condition. The SIF range depends on crack orientation, crack length to Hertzian contact zone half-width ratio, friction between the crack faces and friction on the contact surface. The results were combined in two compact functions that determine the ΔK_I and ΔK_II values. The crack propagation mode and direction were investigated using both the maximum stress criterion and the minimum strain energy density criterion. The results are displayed in graph form, which allows a fast evaluation of the crack growth condition.     

An experimental analysis of displacement field of mixed mode crack

In this paper, the characteristic properties ofv (y-direction displacement) field surrounding the tip of a mixed mode crack are studied. These properties can be used to evaluate the rigid body rotation of the crack tip, theK _I SIF and the ratio ofK _II SIF toK _I.The authors employ a film to record the displacement information based on the technique of moire interferometry with sticking films. By using the data taken from the moire pattern and treating them with the damping least square method, all of the parameters of the crack can be obtained accurately.     

钢轨表面剥离掉块路径预测研究

轮轨滚动接触下,钢轨表面会产生典型的鱼钩形剥离掉块,其形成机理目前暂未明确.为了探究轮轨滚动接触下钢轨表面裂纹扩展机理,基于最大周向拉应力准则,建立轮轨滚动接触疲劳计算模型,提出裂尖扩展路径预测方法,并对不同初始角度裂纹的扩展路径进行预测.结果表明,钢轨表面微裂纹为Ⅰ-Ⅱ复合型裂纹,随着裂纹长度增加,KⅠ先增加后减小,...     

Numerical simulation of stress intensity factors via the thermoelastic technique

The purpose of this study is to investigate the accuracy of the least squares method for finding the in-plane stress intensity factorsK _I andK _II using thermoelastic data from isotropic materials. To fully understand the idealized condition ofK _I andK _II calculated from thermoelastic experiments, the total stress field calculated from finite element analysis is used to take the place of data obtained from real thermoelastic experiments. In the finite element analysis, theJ-integral is also calculated to compare with (K _I ² +K _II ² )/E evaluated by the least squares method. The stress fields near the crack tip are dominated by the two stress intensity factors; however, the edge effect will cause inaccuracy of the thermoelastic data near the crack tip. Furthermore, the scan area of thermoelastic experiments cannot be too small. Therefore, we suggest that three or four terms of stress function be included in the least squares method for evaluating stress intensity factors via the thermoelastic technique. In the idealized condition, the error can be smaller than 3 percent from our numerical simulations. If only ther ^–1/2 term (K _I andK _II ) is included in the least squares method, even in the idealized case the error can be up to 20 percent.     

Thermoelastic investigations for fatigue life assessment

An investigation is presented on the suitability and accuracy of a thermoelastic technique for the analysis of fatigue cracks. The stress intensity factor ranges ΔK _I and ΔK _II are determined from thermoelastic data recorded from around the tip of a sharp slot in a steel specimen under biaxial load, in order to assess the accuracy of the technique. ΔK _I and ΔK _II are determined to within 4% and 9% of a theoretical prediction, respectively. The results from a similar test on a fatigue crack under biaxial load are also presented. These show that thermoelastic stress analysis is a rapid and accurate way of analyzing mixed-mode fatigue cracks. A discussion is given on the potential of thermoelastic stress analysis of propagating cracks.     

A photoelastic study of energy loss during a fracture event

Static and dynamic photoelastic experiments were conducted to evaluate the energy lost due to damping in a thick-walled-ring specimen during a run-arrest fracture event. Short starter cracks were machined into a series of ring specimens fabricated from Homalite 100 and the specimens were loaded by a specially designed mechanical deformeter to giveK _Q/K_Imranging from 1.76 to 2.15. The crack was initiated and high-speed photographs of the isochromatic-fringe loops at the tip of the running crack were recorded. The data were analyzed to obtain the instantaneous stress-intensity factorK(t), the normalized crack positiona/w, and the crack velocity \(\dot a\) . A comparison ofK, as a function of positiona/w, was made between static and dynamic crack growth. Average values ofK were determined from these curves and estimates of initial strain energy and energy lost in forming the fracture surface were made. An energy balance was used to evaluate the energy loss due to damping in all the experiments. The energy loss during the run-arrest event was approximately 50 percent of initial strain energy.     

Influence on fiber inclination and interfacial conditions on fracture in composite materials

Dynamic photoelasticity has been used to study the effect of the fiber-matrix interface and fiber orientation on dynamic crack growth in fiber composites. Two types of fiber-matrix interfaces are considered: well bonded and partly debonded. The fiber-matrix interface is characterized by conducting fiber pullout tests. Partly debonded fibers aligned with the loading direction, result in higher fiber debonded lengths, lower dynamic stress-intensity factorK _ID and lower fracture surface roughness compared to well bonded fibers. Orientation of brittle fibers, with respect to the loading direction, impairs their ability to lowerK _ID , while oriented ductile fibers produce no significant change inK _ID . Misalignment of fibers from the loading direction reduces the fiber debonded length due to kinding of the fiber at the crack face.     

Mixed Mode Dynamic Fracture in Particulate Reinforced Functionally Graded Materials

A detailed analytical and experimental investigation is presented to understand the dynamic fracture behavior of functionally graded materials (FGMs) under mode I and mixed mode loading conditions. Crack-tip stress, strain and displacement fields for a mixed mode crack propagating at an angle from the direction of property gradation were obtained through an asymptotic analysis coupled with a displacement potential approach. This was followed by a comprehensive series of experiments to gain further insight into the behavior of propagating cracks in FGMs. Dynamic photoelasticity coupled with high-speed photography was used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the FGMs. Dynamic fracture experiments were performed using different specimen geometries to develop a dynamic constitutive fracture relationship between the mode I dynamic stress intensity factor (K _ID ) and crack-tip velocity ( ) for FGMs with the crack moving in the direction of increasing fracture toughness. A similar -K _ID relation was also obtained for matrix material (polyester) for comparison purposes. The results obtained show that crack propagation velocities in FGMs were about 80% higher than the polyester matrix. Crack arrest toughness was found to be about 10% lower than the value of local fracture toughness in FGMs.     

Measurement of stress-intensity factor by means of a-c potential drop technique

A loading effect on a-c potential difference measured for two-dimensional stationary surface crack is examined under opening load without shear. An increment of potential difference caused by a load change is revealed to have a proportional relationship with an increment of the stress-intensity factor,K _I. Also, the constant of proportionality of the relationship is found to be independent of the crack length. Based on this relationship, a procedure is developed for measurement ofK _Iby means of the a-c potential drop technique.     

Influence of indenter geometry on half-plane with edge crack subjected to fretting condition

An edge crack is analyzed to study fretting failure. A flat punch with rounded corners and a half-plane are regarded as an indenter and a substrate, respectively. Plane strain condition is considered. Contact shear traction in the case of partial slip is evaluated numerically. It is assumed that an initial crack is extended to the point of minimum strain energy density in the half-plane from the trailing edge of contact. Dislocation density function method is used to evaluate K_I and K_II. The variations of K_I and K_II during crack growth are examined in the case of indentation by a punch with different ratio of the flat region (l) to the punch width (L). Sih's minimum strain energy density theory [1] is also applied to predict the propagation direction of the initial crack. The direction evaluated is similar to that found in the experiment. Stress intensity factor ranges (ΔK_I and ΔK_II) are examined during cyclic shear on the contact. For the design of contacting bodies, a suggestible geometry of punch for alleviating cracking failure is studied.     

Analysis of dynamic mixed-mode isochromatics

The mixed-mode, elastodynamic state of stress in the neighborhood of a constant-velocity crack tip is used to generate numerically unsymmetric isochromatics. Unsymmetry associated with the third-order terms of a mixed-mode stress field, with and without the Mode II singular stress term, is also investigated. In extractingK _I from an unsymmetric isochromatic pattern, errors in the Mode I fracture parameters due to the assumed presence ofK _II in aK _I stress field were found to be significant when data are taken more than 4 mm from the crack tip. Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

Strain-gage methods for measuring the opening-mode stress-intensity factor,K I

Measurements of strain near a crak tip with electrical-resistance strain gages do not usually provide a reliable measure ofK _I because of local yielding, three-dimensional effects and limited regions for strain-gage placement. This paper develops expressions for the strains in a valid region removed from the crack tip, and indicates procedures for locating and orienting the gages to accurately determineK _I from one or more strain-gage readings.     

Study of pure and mixed-mode fracture of a brittle material

In order to study the behavior of a crack in a linear-elastic material in plane mixed mode (modes I+II), a specimen's shape and loading have been specially adapted. The specimens are first precracked in mode I and then subjected to monotonic loading until instability is reached by an original device which makes it possible to control the nature of the mixed mode applied and which is adjustable from pure mode I to pure mode II. After the specimens are fractured, the lengths of the initial cracks and the kinking angles were measured in the plane-strain area. Then the stress-intensity factorsK _I andK _II at the moment when crack instability appeared were calculated. This made it possible to apply two criteria: maximum principal stress and maximum stressintensity factorK ₁ ^* at the onset of kinking. From comparing the calculated values with the experimental values we may note that there is good agreement with respect to the crackkinking directions. However, for the limit load values considerable divergences have been recorded which are analyzed.     

A method for measuring mode I crack tip constraint under static and dynamic loading conditions

A novel experimental technique for measuring crack tipT-stress, and hence in-plane crack tip constraint, in elastic materials has been developed. The method exploits optimal positioning of stacked strain gage rosette near a mode I crack tip such that the influence of dominant singular strains is negated in order to determineT-stress accurately. The method is demonstrated for quasi-static and low-velocity impact loading conditions and two values of crack length to plate width ratios (a/W). By coupling this new method with the Dally-Sanford single strain gage method for measuring the mode I stress intensity factorK _I , the crack tip biaxiality parameter is also measured experimentally. Complementary small strain, static and dynamic finite element simulations are carried out under plane stress conditions. Time histories ofK _I andT-stress are computed by regression analysis of the displacement and stress fields, respectively. The experimental results are in good agreement with those obtained from numerical simulations. Preliminary data for critical values ofK _I and β for dynamic experiments involving epoxy specimens are reported. Dynamic crack initiation toughness shows an increasing trend as β becomes more negative at higher impact velocities.     

Embedded fine-grid method applied to three-dimensional stress-intensity-factor analysis

The purpose of this paper is to extend the embedded fine-grid method to three-dimensional stress-intensity-factor analysis. The embedded crossed fine grids give two components of displacement and are capable of calculatingK _I without the assumption of the plane-strain condition along a crack or a notch front. It is not valid to assume the plane-strain condition to calculateK _I in the vicinity of a free surface, whereK _I is influenced by a free surface (plane-stress condition). In this paper, a dyeing and bleaching process is considered to reproduce the crossed fine grids on an epoxy plate. By using these grids as embedded grids, the distributions ofK _I along notch fronts in SEN specimens with various different thicknesses and side grooves are studied. The influences of a free surface and the side-groove effects on the distribution ofK _I are discussed. Paper was presented at 1982 SESA/JSME Spring Meeting held in Oahu and Maui, HI on May 24–29.     

Rail web fracture in the presence of residual stresses

A recent accident involving roller-straighened alloy rail has raised the question of the safety of such rails. This work shows that the residual stresses in roller-straightened rail can indeed self-drive a long web crack. Specifically, the stress intensity K_I due to release of the key component, longitudinal stress, if of the order of the critical stress intensity for initiation K_Ic for both plain carbon and alloy rail. At cut ends, the resulting vertical residual stresses can give rise to K_Ic if there are 0.1–1 in (3–25 mm) cracks. In this work, checks of the existing residual stress data for self-consistency suggest that the data are only accurate within a factor of two. Therefore, a more direct method is proposed for measuring K_I on a web crack by saw-cutting the web.     

On the determination of the å-K relationship for birefringent polymers

Methods of utilizing dynamic photoelasticity with fracture-type specimens to simultaneously determine the stress-intensity factorK _Iand the crack-tip velocity are reviewed. Problems associated with data analysis to obtainK _Ifrom isochromatic-fringe loops are discussed. Errors resulting from the use of static near-field equations in the method of analysis are considered and a correction method is developed. Finally, the invariance ofK _Im(the minimumK required to maintain a finite crack velocity) is noted and evidence is provided to indicate thatK _Imcan be treated as a material propertly.Paper was presented at 1978 SESA Spring Meeting held in Wichita, KS on May 14–19.