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.     

Simultaneous measurements of stress intensity and toughness for fast-running cracks in steel

Simultaneous measurements of the dynamicstress-intensity factorK _I ^dyn and the dynamic-fracture toughnessK _ID were made in a high-strength steel to investigate the relation between energy delivered to and energy absorbed by rapidly propagating cracks. Values ofK _I ^dyn were obtained intermittently during the propagation history by the shadow optical method of caustics from high-speed photographs of the moving crack tips. Values ofK _ID were calculated from temperature maxima recorded by thermocouples near the crack path. The results indicate that for fast-running cracks, the change in energy available at the crack tip can be significantly less than the energy absorbed in crack extension, suggesting that currently used dynamic-energy-balance methods for determining dynamic-fracture toughnesses may provide erroneous values.     

Analytical and experimental determination of dynamic impact stress intensity factor for 40 Cr steel

A linear elastic three-dimensional finite element analysis is made to analyze the near field stress behavior of an edge cracked rectangular bar simply supported and subjected to central impact at the back side of the crack. The material is made of 40 Cr steel. Determined numerically are the local time histories of the stress wave, displacement near load point, crack tip strain, and dynamic stress intensity factor K_(d)¹. The above quantities were also measured experimentally by performing impact tests; they agreed well with the analytical results and determine the load at fracture initiation and hence the critical dynamic stress intensity factor K_(d)^1c. The interaction effect between the loading bar and specimen appears to be negligible.     

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.     

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.     

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.     

Determination of the dynamic stress intensity factorsK I d andK II d,for a mixed-mode propagating crack

In this paper, the dynamic propagation problem of a mixed-mode crack was studied by means of the experimental method of caustics. The initial curve and caustic equations were derived under the mixed-mode dynamic condition. A multi-point measurement method for determining the dynamic stress intensity factors,K _I ^d , andK _II ^d , and the position of the crack tip was developed. Several other methods were adopted to check this method, and showed that it has a good precision. Finally, the dynamic propagating process of a mixed-mode crack in the three-point bending beam specimen was investigated with our method.     

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.     

Stress intensity factor and crack velocity relationship for polyester/TiO2 nanocomposites

The dynamic fracture behavior of polyester/TiO₂ nanocomposites has been characterized and compared with that of the matrix material. A relationship between the dynamic stress intensity factor,K _I and the crack tip velocity,å, has been established. Dynamic photoelasticity coupled with high-speed photography has been 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 nanocomposites. Single-edge notch tension and modified compact tension specimens were used to obtain a broad range of crack velocities. Fractographic analysis was conducted to understand the fracture process. The results showed that crack arrest toughness in nanocomposites was 60% greater than in the matrix material. Crack propagation velocities prior to branching in nanocomposites were found to be 50% greater than those in polyester.     

平面应变下紧凑拉伸试样的动态断裂韧性的实验研究

材料的动态断裂韧性是衡量材料在动载荷作用下抵杭裂纹扩展能力的重要指标,以往的材料动态断裂韧性测试多采用三点弯曲试样,而针对紧凑拉伸试样的动态断裂韧性研究很少.本文将紧凑拉伸试样(即CT试样)简化成等效弹簧质量模型,得到了CT试样动态应力强度因子的近似表达式.对Hopkinson压杆装置进行了改进,利用改进后的实验装置进...     

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.     

A study ofJ-integral of the orthotropic composite material

The relation between J-integral near model I crack tip in the orthotropic plate and displacement derivative is derived in this paper. Meanwhile, the relation between stress intensity factor K _I and displacement is also given in this paper. With sticking film moire interferometry method, the three-point bending beam is tested, thus the values of J-integral and K _I can be obtained from the displacement field, and then the truth of relation formula between J-integral and K _I in the orthotropic composite materials is experimentally verified.     

Dynamic stress-intensity factors for unsymmetric dynamic isochromatics

The mixed mode, near-field state of stresses sourrounding a crack propagating at constant velocity is used to derive a relation between the dynamic stress-intensity factorsK _I,K _II, the remote stress component σ _ox and the dynamic isochromatics. This relation, together with an over-deterministic least-square method, form the basis of a datareduction procedure for extracting dynamic,K _I,K _II and σ _ox from the recorded dynamic photoelastic pattern surrounding a running crack. The overdeterministic least-square method is also used to fit static isochromatics to the numerically generated dynamic isochromatics. The resultant staticK _I,K _II and σ _ox are compared with the corresponding dynamic values and estimats of errors involved in using static analysis to process dynamic isochromatic data are obtained. The data-reduction procedure is then used to evaluate the branching stress-intensity factor associated with crack branching and the mixed-mode stress-intensity factors associated with crack curving.     

Effect of T-stress on crack growth under mixed mode I–III loading

For a crack subjected to combined mode I and III loading the influence of a T-stress is analyzed, with focus on crack growth. The solid is a ductile metal modelled as elastic–plastic, and the fracture process is represented in terms of a cohesive zone model. The analyzes are carried out for conditions of small scale yielding, with the elastic solution applied as boundary conditions on the outer edge of the region analyzed. For several combinations of the stress intensity factors K_I and K_III and the T-stress crack growth resistance curves are calculated numerically in order to determine the fracture toughness. In all situations it is found that a negative T-stress adds to the fracture toughness, whereas a positive T-stress has rather little effect. For given values of K_I and T the minimum fracture toughness corresponds to K_III = 0.     

FEM analysis on mixed-mode fracture of CSM-GRP

A FEM analysis for studying mixed-mode fracture problem of chopped strand mat glass fibre reinforced polyester laminate is presented. The analysis is formulated on the basis of 8-node quadrilateral isoparametric element. The collapsed triangular quarter-point singular elements were used for calculating stress intensity factors K_Ι and K_Ⅱ.The crack propagation process was computed by implementing constraint release technique. Three different approaches to the solution of stress intensity factors K_Ι and K_Ⅱ were compared. The effect of constraint condition imposed upon the displacement of the three collapsed nodes of the crack tip elements on the K_Ι and K_Ⅱ results was evaluated. The mixed-mode critical stress intensity factors K_ΙC and K_ⅡC were estimated for CSM-GRP through the consideration of K_Ι and K_Ⅱ calculated and the measured failure load and critical crack length in the experiment.     

Crack growth rate and cracking velocity in fatigue for a class of ceramics

Fatigue crack growth rate data and cracking velocity data are studied for a class of ceramics including SiC, TiB₂, Si₃N₄, ZrO₂ and Al₂O₃. Both sine and square wave cyclic loading are combined such that the data could be converted to cracking velocity for a given frequency of cyclic load. An effective stress intensity factor range is defined and used in an relation for computing the crack growth rate and cracking velocity. As for the metal alloys, the data for ceramics also fall into three regimes identified with near-threshold, stable growth and rapid crack extension, except that the slope of the da/dN (the crack growth rate) curves for ceramics are steeper in comparison with that for metals. Reported are the empirical constants in the relations for the crack growth rate and the cracking velocity for a variety of ceramics.     

Dynamic fracture behavior of ceramics at elevated temperatures by caustics

The fracture behavior of partially stabilized zirconia (PSZ) and silicon-nitride ceramics (Si₃N₄) is investigated under dynamic loading at elevated temperatures up to 1200°C using the caustic method combined with an ultra high-speed camera. The values of the dynamic fracture toughnessK _Id and the crack-propagation fracture toughnessK _ID are obtained, and it is shown that a dynamic effect on these values is observed in PSZ but not in Si₃N₄. The dynamic crack arrest toughnessK _Ia is found to exist for PSZ.     

An Experimental Study of Mixed Mode Crack Initiation and Growth in Functionally Graded Materials

Quasi-static mixed mode crack initiation and growth in functionally graded materials (FGMs) was studied through fracture experiments on polymer-based FGMs manufactured by selective ultraviolet irradiation poly(ethylene carbon monoxide)—a photo-sensitive copolymer that becomes more brittle and stiffer under ultraviolet irradiation. The objective of the study was to determine whether crack kinking criteria for homogeneous materials, e.g., maximum hoop stress criterion, also hold for FGMs. Single edge notched tension specimens with different spatial variations of Young's modulus, failure stress and failure strain, were tested. Near tip mode mixity was introduced either by inclining the crack to the remote loading direction, as in the case of homogeneous materials, or to the direction of material gradient, or both. 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, and to extract the fracture parameters of stress intensity factor K _I and K _II , and the T-stress. It was found that the nonsingular T-stress term in the asymptotic expansion for stresses plays a very important role in accurately measuring fracture parameters. It was also found that the maximum tangential stress criterion can be applied to the case of FGMs to predict crack kinking provided that the effect of the T-stress is accounted for and the process zone size is small compared to the intrinsic material gradient length scale. However, for accurate crack path prediction at a length scale comparable to the material gradient, detailed material property information is required. In general, the crack will propagate towards a region that exhibits less fracture toughness, but, unlike the case of homogeneous materials, along a path where K _II is not necessarily equal to zero.     

Fracture-toughness testing of limestone

Fracture-toughness measurements were made on standard three-point-bend fracture specimens of Indiana limestone. Specimen dimensions, experimental techniques, and methods of data reduction were chosen to comply as closely as possible to the Tentative Method of Test for Plane Strain Fracture Toughness of Metallic Materials (ASTM Designation: E399-72T). Typical strain-gage-type clip-in displacement gages were found to lack the necessary sensitivity for measuring the crack-opening displacement while an LVDT displacement transducer having a linear range of ±0.25 mm (±0.010 in.) was found to be ideal.Fatigue cracks were successfully introduced by repeated cycling to 85 percent of the fracture load. Load vs. crack opening-displacement records indicated that crack closure occurred in these tests. Effective crack lengths were determined using an experimental compliance calibration that was checked analytically. Final fracture was stable when using displacement control in a stiff load frame. Some size effects were noted, with toughness increasing with specimen size. Values ofK _c, fracture toughness, were found to approach 990 kNm^–3/2 (900 .) for the largest specimens.Paper was presented at 1975 SESA Spring Meeting held in Chicago, IL on May 11–16.Work was supported by the U.S. Energy Research and Development Administration.     

Strain strengthening effects in Witwatersrand quartzite

A series of uniaxial compression specimens were tested over a range of applied ram displacement rates of 8.9 × 10⁻⁴ to 8.9 mm/sec to elucidate the effects of loading rate on the uniaxial compressive fracture stress of Witwatersrand quartzite. It was demonstrated that even within standard loading rate ranges, considerable scatter in the fracture strength (under uniaxial compression) existed in this particular quartzite rock. Nevertheless, a definite trend of increasing fracture resistance with increasing monotonic loading rate was evident inasmuch that increasing the loading rate (strain rate) by four orders of magnitude increase the fracture strength by almost 2.8 times. Prior fatigue loading also produced a significant strain strengthening as the uniaxial compressive fracture stress tended to increase in a sigmoidal fashion with increasing number of fatigue cycles prior to testing. Indeed, the fracture strength of quartzite was almost doubled in value after 10⁻ cycles. Plane strain fracture toughness tests utilising three point bend specimens were conducted and an average of K_lc = 1.7 MPa√m was realized. In both the uniaxial compression tests and the fracture toughness tests, failure occurred by crack extension predominantly by a transgranular flat cleavage-like mode through pure quartzite (silica) regions. However, crack extension was also observed to occur in an intergranular “ductile-like” mode through areas associated with inclusions prevalent in the quartzite.