Showing papers on "Fracture toughness published in 1977"

Finite deformation analysis of crack-tip opening in elastic-plastic materials and implications for fracture

Abstract: A nalyses of the stress and strain fields around smoothly-blunting crack tips in both non-hardening and hardening elastic-plastic materials, under contained plane-strain yielding and subject to mode I opening loads, have been carried out by use of a finite element method suitably formulated to admit large geometry changes. The results include the crack-tip shape and near-tip deformation field, and the crack-tip opening displacement has been related to a parameter of the applied load, the J -integral. The hydrostatic stresses near the crack tip are limited due to the lack of constraint on the blunted tip, limiting achievable stress levels except in a very small region around the crack tip in power-law hardening materials. The J -integral is found to be path-independent except very close to the crack tip in the region affected by the blunted tip. Models for fracture are discussed in the light of these results including one based on the growth of voids. The rate of void-growth near the tip in hardening materials seems to be little different from the rate in non-hardening ones when measured in terms of crack-tip opening displacement, which leads to a prediction of higher toughness in hardening materials. It is suggested that improvement of this model would follow from better understanding of void-void and void-crack coalescence and void nucleation, and some criteria and models for these effects are discussed. The implications of the finite element results for fracture criteria based on critical stress or strain, or both, is discussed with respect to transition of fracture mode and the angle of initial crack-growth. Localization of flow is discussed as a possible fracture model and as a model for void-crack coalescence.

The essential work of plane stress ductile fracture

Abstract: In a ductile material, the total work of fracture is not a material constant and linear fracture mechanics is inappropriate. The work performed in the end region at the tip of a crack, where the fracture process takes place, is considered the essential work of fracture, and a constant for a particular sheet thickness. It is shown that this essential work can be estimated from deep edge notched tension specimens by extrapolating the straight line relationship between the work of fracture and ligament length to zero ligament length.

Crack Growth During Low-Cycle Fatigue of Smooth Axial Specimens

Abstract: Crack growth data are reported for small axially loaded smooth specimens of A533B steel subjected to strain cycling fatigue at large plastic strains. Surface crack lengths were monitored using cellulose acetate replicas, and occasional specimens were broken open to determine crack depth. Experimental crack growth rates for different strain levels are correlated in fracture mechanics fashion by the J integral concept, with J values being estimated from stress-strain hysteresis loops. The crack growth rate data of this investigation are compared with previous data for the same material obtained from linear elastic fracture mechanics tests. It is suggested that research on the behavior of small cracks is fundamental to a better understanding of the fatigue process.

Experimental Verification of the J Ic and Equivalent Energy Methods for the Evaluation of the Fracture Toughness of Steels

Abstract: The critical value J 1 c and the apparent fracture toughness K B d are measured with a single small specimen (compact tension or three-point-bend bar) loaded in the elastic-plastic range. Initiation is detected during loading by an electrical potential method. For the steels studied here (2.25Cr-lMo, electroslag weld, manganese cast steel), the K 1 c values deduced from J 1 c are in agreement with the K 1 c values directly measured with thick specimens in the transition-temperature range. Furthermore, the equivalent energy procedure gives the same results as those obtained by the J-integral method.

Measurements of dynamic stress intensity factors for fast running and arresting cracks in double-cantilever-beam specimens

Abstract: The influence of dynamic effects on the crack arrest process is investigated. For propagating and subsequently arresting cracks, actual dynamic stress intensity factors were measured applying a shadow optical technique incombination with a Cranz Schardin high-speed camera. The experiments were performed in wedge-loaded double-cantilever-beam (DCB) specimens machined from an epoxy resin (Araldite B). In the initial phase of crack propagation the measured dynamic stress intensity factors were found smaller; in the arresting phase, however, they were larger than the corresponding static values. After arrest the dynamic stress intensity factor oscillates with decreasing amplitude around the static stress intensity factor at arrest. Crack arrest toughness values determined according to a static analysis showed a dependence on the crack velocity prior to arrest, but the dynamic crack arrest toughness yielded a single value only, indicating that this quantity represents a true material property.

Crack-tip fields in steady crack-growth with linear strain-hardening

Abstract: Singular stress and strain fields are found at the tip of a crack growing steadily and quasi-statically into an elastic-plastic strain-hardening material. The material is characterized byJ2 flow theory together with a bilinear effective stress-strain curve. The cases of anti-plane shear, plane stress and plane strain are each considered. Numerical results are given for the order of the singularity, details of the stress and strain-rate fields, and the near-tip regions of plastic loading and elastic unloading.

Instability of cracks under impulse loads

Abstract: A plate impact method was used to produce internal penny‐shaped cracks in polycarbonate and to study the response of these cracks to short tensile pulse loads. The observed crack instability behavior could not be explained by classical static fracture mechanics. A short‐pulse fracture mechanics was developed from static fracture mechanics concepts. The instability criterion was obtained from considerations of the early time stress intensity histories experienced by cracks struck by short‐pulse loads. This criterion, which requires that the dynamic stress intensity exceed the dynamic fracture toughness for a certain minimum time, gave results in accord with the experimental data. Short‐pulse fracture mechanics defines the conditions for which simple static expressions can be used to determine dynamic fracture toughness. The dynamic fracture toughness of polycarbonate at a stress intensification rate of 107 MN m−3/2 sec−1 was measured to be 2.2±0.2 MN m−3/2, about 60% of the quasistatic value. This result supports the view that material toughness does not increase sharply at high loading rates, but rather decreases monotonically with increasing stress intensification rate until a constant minimum value is reached.

Metallurgical factors affecting the crack growth resistance of a superalloy

Abstract: During creep loading of IN-792, grain boundary morphology in conjunction with grain size strongly affected crack propagation. Compositional variations and fabrication techniques showed no significant effect. A primary requirement for materials to be used in gas turbine engine discs is satisfactory resistance to crack growth resistance in the 650 to 760°C range. Both conventional smooth and machine notched stress-rupture samples and dead weight loaded fatigue precracked fracture toughness specimens were evaluated in this study. Creep fractures took place by grain boundary cracking followed by rapid transgranular fractures. Composition variations had only very slight effects on crack propagation. Materials hot worked from castings had the same properties as those made by powder metallurgy techniques. The primary factors influencing the crack growth behavior were the grain size and grain shape. Increasing grain size markedly improved the toughness. By slow cooling through the gamma prime solvus a serrated grain boundary structure was developed that also improved the cracking resistance. Earlier creep fracture toughness studies have shown that the slow crack growth behavior can be described by a critical strain model in which the crack propagation is controlled by the yield strength, grain size, and a critical strain parameter. The present results are consistent with this model, with serrated grain boundaries introducing a four-fold increase in the critical strain parameter over that of smooth grained material.

Fracture at elevated temperature

Abstract: We have carried out a systematic experimental study of fracture in materials which contain hard second phase particles. The principal variables in this study were the average size and spacing of the second phase particles, grain size, temperature, and the strain rate. Polycrystalline copper containing a dispersion of silica particles was the material used in these experiments. Three modes of fracture were observed: transgranular necking fracture, fracture by the propagation of intergranular cracks initiated at the surface, and intergranular fracture by grain boundary cavitation throughout the entire specimen cross-section. The transition between the fracture modes was shown to shift systematically with temperature, strain rate, and the microstructure. The intergranular fracture mode was studied in detail. The growth of cavities in the grain boundaries was determined to be the rate limiting step in the fracture process. It was determined that in the range of 10-4 to 10-7 s-1 in strain rate, the dominant growth mechanism of the cavities was power-law creep rather than diffusional transport. The ductility of the material in the intergranular mode of fracture was found to be strongly dependent on the area fraction of the second phase in the grain boundary and on the strain rate sensitivity of the material; it was weakly dependent on the grain size. A theoretical lower bound and a practical upper bound of the ductility in the intergranular fracture mode were established. The results are in qualitative agreement with the data on nickel-base alloys and other materials published in the literature.

Correlation of microstructure with mechanical properties of 300m steel

Abstract: 300M steel was subjected to a wide range of quenched and tempered heat treatments. The plane-strain fracture toughness and the tensile ultimate and yield strengths were evaluated. Results indicate that substantial improvement in toughness with no loss in strength can be accomplished in quenched and tempered steel by austenitizing at 1255 K (1800°F) or higher. Low fracture toughness in conventionally austenitized 300M steel (1144 K (1600°F)) appears to be caused by undissolved precipitates seen both in the submicrostructure and on the fracture surface which promote failure by quasi-cleavage. These precipitates appeared to dissolve in the range 1200 to 1255 K (1700 to 1800°F).

Fracture characteristics of acrylic bone cements. II. Fatigue

Abstract: The vital first phase of the overall materials study to protract the life of total joint replacements is the identification of the fracture toughness and fatigue properties of bone cements. Information gained from fatigue testing, performed in a manner which simulates in vivo conditions, and fracture toughness, which is a measure of the propensity of a crack to propagate, is the first step towards the prediction of the life of the total joint replacement. Part I of this study identified the fracture toughness characteristics of two acrylic bone cements, while the present work has been concerned with determining the fatigue behavior by means of tests conducted in a rotating bending fatigue apparatus. Fatigue specimens were fabricated under conditions which approximated clinical procedures and then tested while immersed in bovine serum at 37°C in order to simulate in vivo conditions. In addition, a similar study was completed on specimens tested in air at ambient temperature for purposes of comparison. Testing was conducted in both of these environments on specimens containing zero and 10.0 wt % BaSO4. Cyclic loading frequency was maintained between 1200 and 1400 cycles/min in order to insure that crack propagation was the sole mechanism of failure, i.e., failure via cyclic thermal softening was obviated. Results of this phase of the study, when analyzed by a Student t-test at the 90% confidence level with four degrees of freedom, indicate that the fatigue life of specimens tested in bovine serum at 37°C is superior to that of specimens tested in air at ambient temperature. The addition of BaSO4 to Simplex-P cement, while not significant at the 90% confidence level, was significant in increasing the fatigue life in air at the 80% confidence level; however, this effect was not noticeable when testing in bovine serum at 37°C. Examination of the fracture surfaces enabled calculation of the critical stress intensity factor which when compared with values from an earlier work showed good agreement.

Fatigue under complex stress

Abstract: Fatigue-crack propagation in biaxially stressed plates has been investigated. The normal stress σx, applied on a plane perpendicular to the crack front, affects the rate of propagation of a Stage II crack extending by a Mode I mechanism. This stress, which does not affect singularity conditions in a linear elastic fracture mechanics analysis, has different effects should it be tensile or compressive, cyclic or constant. The changes in crack-growth rate are related to changes in the size of the plastic shear ears at the tip of the crack. Fatigue-crack propagation is related to two parameters in the plane of the plate, the maximum shear stress range and the stress normal to the plane of maximum shear. Both these parameters will affect the crack-opening displacement and hence crack-growth rate.

Observations on the effect of cementite particles on the fracture toughness of spheroidized carbon steels

Abstract: The results of experimental studies of the influence of cementite particles on the fracture toughness of a number of spheroidized carbon steels at low temperatures were analyzed in terms of current theories of crack-tip behavior. The fracture toughness parameterKIC was evaluated by using circumferentially notched and fatigue-cracked cylindrical specimens. The conclusions are summarized as follows: 1) In general,KIC decreases with increasing volume fraction and increasing size of the carbide particles. 2) Crack initiation occurs at the carbide particles. 3) Crack propagation occurs by cleavage if the stress conditions satisfy the Ritchie, Knott and Rice criterion that a critical cleavage stress is achieved over a minimum microstructural size scale. The critical stress is that required to propagate a crack from a particle and the minimum size scale is of the order of 1 to 2 grain sizes. 4) Crack propagation occurs initially by fibrous rupture if the stress intensification is insufficient to attain the critical cleavage stress.

A theory of the initiation of creep crack growth

Abstract: A computer simulation of the time dependent development of the plastic zone ahead of a crack loaded in uniform tension was performed. The material was assumed to deform according to a creep law relating the local strain rate to the local stress. The plastic zone was modelled by an array of edge dislocations coplanar with the crack. For a given time the stress was found to be uniform in a region ahead of the crack. This region increased and the local stress decreased with increasing time. The distribution of dislocations in the zone at a given time was found to be almost the same as that given by the Bilby, Cottrell and Swinden model (1963) if the friction stress in that model was replaced by an apparent friction stress equal to the uniform stress ahead of the crack. This apparent friction stress is dependent on both the applied stress and time. Assuming a critical crack opening displacement (COD) or a critical value of theJ integral,J c, to be the criteria for the onset of the creep crack growth the initiation time can be calculated using the results of this study. A good agreement between the theory and experiment is obtained for two different CrMoV steels. This comparison with experiments suggests that the COD is an appropriate crack growth initiation parameter for both ductile and brittle materials whilstJ cdoes not seem to be applicable in creep fracture.

Interrelations between fracture toughness and other mechanical properties in titanium alloys

Abstract: Critical stress intensity factors and general tensile properties were measured for a class of metastable beta and alpha-beta titanium alloys with a limited number of compositions but processed to have a wide variety of strength levels and microstructures. These data were used to test thirteen theoretical relations between the fracture toughness and tensile parameters. Many of the theoretical relations had been proposed previously, but several new forms were derived in the present work. The correlation showed that for alloys exhibiting a limited range of microstructures, the simpler correlations gave the better fits withK Ic α γ−1specifically being the best one. For correlations of alloys with a wide range of microstructures, more complex correlations which included microstructural parameters were found to be superior.

Generalized fracture mechanics

Abstract: According to Andrews' generalized fracture mechanics theory [1], the fracture energy of a solid is given by l= l0Φ where l0 is a surface energy and Φ a loss function whose form is explicit The loss function has been evaluated experimentally for four highly extensible materials, styrenebutadiene rubber, ethylene-propylene rubber, plasticized PVC and polyethylene and at various rates of crack propagation The quantity l0 has also been calculated from existing theory and a prediction thus obtained for fracture energy The results indicate good agreement between experiment and theory and thus appear to corroborate the generalized formulation of fracture mechanics in its application to non-linear inelastic materials

The impact fracture behaviour of notched specimens of polycarbonate

Abstract: The impact fracture behaviour of notched specimens of polycarbonate has been studied for a range of notch tip radii. For razor-notched specimens a simple fracture toughness analysis is appropriate, as shown by previous workers. Very blunt notches also give constant fracture toughness values, but at a much higher level, corresponding to a different mode of failure. For intermediate notch tip radii the situation is much more complex, and comparison of results for two molecular weight grades shows that the behaviour is molecular weight-dependent. Analysis of these results has been discussed either in terms of a combination of plane strain and plane stress fracture modes, or in terms of a critical stress at the root of the notch, which appears to be appropriate in certain cases.

Prediction of threshold stress intensity for fatigue crack growth using a dislocation model

Abstract: It has been shown that the ratio of threshold stress intensity for fatigue crack growth to the shear modulus is nearly a constant for many materials This implies that fatigue crack growth is related to some fundamental phenomenon occurring at the crack tip In the following a dislocation model has been developed to predict the threshold stress intensity It is shown that the stress intensity can be related to the stress necessary to nucleate a dislocation at the crack tip The most important outcome of the present analysis is that the threshold stress intensity depends more on the elastic modulus rather than on any other material property in agreement with many experimental results

Specimen for fracture mechanics studies on glass

Abstract: A convenient specimen for evaluating stress intensity factors versus crack velocities for brittle materials is presented. When the rod is stressed in uniform compression, the hole acts like a stress raiser to initiate two flat cleavage fractures which propagates in a stable way along the plane of symetry of the rod. Easy control of fracture starting or arrest is obtained by simple adjustment of the applied compressive stress. The tests have been performed on three current glasses in five media. Comparison with results given by literature shows on the whole a rather good correspondence.

Fracture Toughness of Composite and Unfilled Restorative Resins

Abstract: Fracture toughness, critical strain energy release rate, and critical stress intensity factor were determined for experimental and commercial restorative resins. A composite resin had lower resistance to crack initiation than an unfilled acrylic resin. The data were consistent with surface failure observed in single-pass wear studies of these resins.