Showing papers on "Strain energy release rate published in 1977"
TL;DR: In this article, a finite element method was used to analyze the deformation field 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.
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.
792 citations
TL;DR: In this article, it was shown that 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.
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.
439 citations
TL;DR: In this article, an experimental and analytical study was conducted to examine the free-edge delamination mode of failure in a (± 30/±30/90/90)S Boron/ Epoxy laminate.
Abstract: An experimental and analytical study was conducted to examine the free-edge delamination mode of failure in a (±30/±30/90/90)S Boron/ Epoxy laminate. The initiation and stable growth of the delamination for static tension loading conditions were identified using ultrasonic tech niques. A finite element representation for the test specimen was con structed using conventional elements. The interlaminar stress distribution at the laminate midplane was found to be in agreement with published results. The finite element representation was used to model the initiation and stable growth of the delamination. An applied force versus longitudinal strain curve was obtained from the model based on the data for the longi tudinal strain versus the extent of the delamination. The applied force versus longitudinal strain curve obtained from the model was between the two sets of data obtained from the specimens. The model also predicted the strain level at which the laminate showed a marked decrease in stiff ness. Energy ...
171 citations
TL;DR: In this paper, a quasi-continuous evaluation of the load-deflection curve recorded during controlled fracture is obtained as a function of the achieved crack length, which may be regarded as the crack extension resistance of the material because the balance between the energy release rateg1 andR is maintained throughout the experiment.
Abstract: Sub-critical crack extension can readily be observed in controlled fracture tests in fourpoint bending. A natural crack of any desired lengthc which exceeds the notch depthc0 by the amount Δc =c −c0 can be introduced into bend specimens by stable crack propagation. The stress intensity factor to achieve Δc increases considerably with increasing Δc. In pre-cracked specimens the stress intensity factorKI0 to start the crack and the critical valueKIC strongly depend on the natural crack length Δc whereasKI0 andKIC are independent ofc0 in solely notched specimens. From a quasi-continuous evaluation of the load-deflection curve recorded during controlled fracture, the “differential work of fracture” can be obtained as a function of the achieved crack length. It may be regarded as the crack extension resistanceR of the material because the balance between the energy release rateg1 andR is maintained throughout the experiment. By that, a formal analogy to theR-curve concept of fracture mechanics is given. The steady increase ofR is explained by multiple crack formation and by the interference of the fracture surfaces due to the angular development of the crack front.
166 citations
TL;DR: A comparison of the experimentally determined effective modulus with theEffective modulus calculated from the transversely isotropic model for bone showed good agreement and a significant positive correlation with dry density was found.
142 citations
TL;DR: In this paper, a short-pulse fracture mechanics was developed from static fracture mechanics concepts, which defines the conditions for which simple static expressions can be used to determine dynamic fracture toughness.
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.
107 citations
TL;DR: In this article, the effect of couple stresses at a crack tip was investigated by considering two particular problems, and it was shown that the energy release rate tends to the classical elastic value as the couple stress (or micropolar) parameter tends to zero.
98 citations
TL;DR: In this article, a method of calculating stress intensity factors for branched and bent cracks embedded in an infinite body has been developed, where the branches are always assumed to be sharp cracks and are modelled by dislocation distributions.
Abstract: A method of calculating stress intensity factors for branched and bent cracks embedded in an infinite body has been developed. The branches are always assumed to be sharp cracks and are modelled by dislocation distributions. The original crack may be either sharp or of elliptical cross-section with finite root radius. Hence, the method which has a precision ±2%, is also applicable to the study of crack branches emanating from elliptical holes and, approximately, also from notches. The following detailed calculations have been made assuming mode I loading: branched sharp crack with branches of equal and different length, bent sharp crack, and one and two crack branches emanating from the crack with a finite root radius. Bending of a sharp crack under mixed mode loading has also been studied. The criteria of maximum tensile stress and maximum energy release rate used in the study of direction of crack propagation are discussed.
81 citations
TL;DR: The validity of the singular solution for the crack tip stress and displacement field in an infinite sheet with a flat line crack with biaxial loads applied to the outer boundaries was investigated in this paper.
74 citations
TL;DR: In this paper, the fracture energy of a solid is given by l = l0Φ where l0 is a surface energy and Φ is a loss function whose form is explicit.
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
64 citations
TL;DR: Fracture toughness, critical strain energy release rate, and critical stress intensity factor were determined for experimental and commercial restorative resins and were consistent with surface failure observed in single-pass wear studies of these 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.
TL;DR: In this paper, a solution for two bonded isotropic linearly elastic halfplanes of different elastic properties having a crack along the interface as welt as a perpendicular crack in one of the half-planes which may intersect the interface crack is given.
TL;DR: In this paper, the authors used boundary-integral equation (BIE) to model three-dimensional fracture mechanics problems using the boundaryintegral equations (BIEs) for surface and corner cracks in gas turbine engines.
Abstract: Efficient and accurate stress analysis methods are required to perform routine fracture mechanics analysis of surface and corner cracks in structures. Such analysis capabilities form the basis of fatigue life predictions for growing cracks in gas turbine engine structures. Boundary-integral equation (BIE) methods offer significant advantages to the fracture mechanics analyst in ease of use, accuracy, and modeling efficiency. Techniques for modeling three-dimensional fracture mechanics problems using the boundary-integral equation method are reviewed. Strain energy release rate modeling, together with crack opening displacement data, are found to give accurate and systematic estimates of crack front stress intensity factor distributions. Accuracy of the techniques are evaluated for well-known buried elliptical crack problems. Numerical models are extended to surface and corner cracks.
TL;DR: In this paper, a nonlinear finite element analysis is performed for a finite center-cracked specimen subjected to biaxial loading, and a Ramberg-Osgood type stress-strain relation is used to characterize the material property.
01 Jun 1977
TL;DR: In this paper, a finite element stress analysis coupled with the strain energy density fracture criterion is proposed to model the ductile fracture behavior in plate specimens, where the last ligament of failure tends to curve developing a cup-and-cone type of fracture in tensile bars and sheer lips.
Abstract: : The phenomenon of ductile fracture in plate specimens is described by a finite element stress analysis coupled with the strain energy density fracture criterion. The last ligament of failure tends to curve developing a cup-and-cone type of fracture in tensile bars and sheer lips in plate specimens. Three-dimensional crack growth profiles are developed by assuming that materials tend to break along the path of minimum strain energy density whose critical value is characteristic of the material and has been measured experimentally for both elastic and plastic materials. The results are encouraging in that ductile fracture behavior can be modeled by holding the strain energy density constant. Hence, allowable load and net section size can be predicted for specimens that deform in the plastic range. (Author)
TL;DR: In this paper, the generalized strain energy release rate derived from an overall energetic balance is a parameter particularly suitable for this problem, and two experimental tests carried out on plates and shells cracked under pressure are described.
01 May 1977
TL;DR: In this paper, the results of notched mortar and concrete prisms tested in compression were presented and discussed, including crack patterns, compressive strain variation, variation of tensile strain at the tip of notch, ultimate strength and critical strain energy release rate of the specimens.
Abstract: The paper presents the results of notched mortar and concrete prisms tested in compression. Crack patterns, compressive strain variation, variation of tensile strain at the tip of notch, ultimate strength and critical strain energy release rate of the specimens are given and discussed.
Journal Article•
TL;DR: In this paper, the authors derived the relations between the earthquake source parameters and the stress conditions in the crust, for strike-slip, dipslip and circular disk-shaped shear faults.
Abstract: The formulas of strain energy release rate and crack sliding displacement pro-pesed in fracture mechanics have been used in the study of earthquake faulting process. Then, by applying the magnitude-energy relation, logee=α1M+α2, the relations between the earthquake source parameters and the stress conditions in the crust, for strike-slip, dip-slip and circular disk-shaped shear faults were derived. The results are summarized in Table 2. For the case of strike-slip fault, they are as follows:(6) The expression for determining regional stress τ0, M0 =where M, magnitude of earthquake; L, W length and width of the fault; tj, seismic efficiency: To, regional shear stress; τy, yielding shear strength; fi, rigidity modulus; v, Poisson Ratio; D, average dislocation and M0, the seismic moment.The yielding strength under the stress condition prevailing in the crust, can be measured in the laboratory, therefore, by means of (6) or (1), the regional shear stress can be esyimated from earthquake data. It can be seen that a considerable difference exists between the relations mentioned above and the relations for the earthquake source parameters in current use. It is because, in the latter case, the initial and final stress condition of the fracture are only taken into consideration, whereas in the former case, the fracture process in the light of fracture mechanics has been dealt with.
TL;DR: In this paper, a general expression for the energy release rate per unit length of crack advance is obtained for three special classes of body shapes: bodies symmetrical about a fiber, bodies bounded on the cracked side by a fiber and bodies bounded by the same fiber on the opposite side.
TL;DR: In this paper, an energy balance criterion based on fracture mechanics concepts is proposed for predicting the loads at which concrete members develop rapidly propagating cracks, and the shape of the growing microcrack zone is determined by the stress intensity factors for the extremities of the principal axes of that zone.
Abstract: An energy balance criterion, based on fracture mechanics concepts, is proposed for predicting the loads at which concrete members develop rapidly propagating cracks. After an initial period during which microcracks increase slowly in length and extent over a critical region of the member, an unstable running crack develops when the rate of energy released by continuing microcrack growth exceeds the energy inputed to the system. The shape of the growing microcrack zone is determined by the stress intensity factors for the extremities of the principal axes of that zone. A critical strain energy release rate, G sub c, is determined from direct tensile data and its appropriateness verified by showing that strength and size effects are correctly predicted for modulus of rupture specimens. Diagonal tension cracking load expressions for reinforced concrete beams are developed using the G sub c value and energy criterion. Those expressions correctly predict the effects estabilished from tests of the moment of shear ratio, reinforcement ratio, type of loading, and size of member. /Author/
TL;DR: In this paper, the authors predict the motion of a penny-shaped crack in a bar of polymethylmethacrylate under uniaxial tension by using numerically calculated values for the strain energy release rate, an analytic expression for the dynamic screening function, and experimentally found data for the velocity dependence of the fracture energy.
Abstract: The strain energy released per unit of axisymmetric crack surface created statically can be expressed in terms of a J-integral related quantity. However, as soon as the crack starts to move only part of this energy will actually flow to the dissipative regions close to the crack tip and the rest will be distributed as kinetic and potential energy in the structure. An energy balance at the crack tip requires that the flow of energy to the tip must be equal to the fracture energy, which for a given material is supposed to be a specific function of the crack-tip velocity. The energy flow is assumed to be expressible as the static strain energy release rate, times a dynamic screening function, which depends on the instantaneous crack-tip velocity only. By using numerically calculated values for the strain energy release rate, an analytic expression for the dynamic screening function, and experimentally found data for the velocity dependence of the fracture energy, it has been possible to predict the motion of a penny-shaped crack in a bar of polymethylmethacrylate under uniaxial tension. The agreement with a small series of simple experiments is good.
01 Jan 1977
TL;DR: In this article, a linear elastic fracture mechanics was used to study longitudinal crack propagation in bovine compact bone and the resistance to crack initiation in slotted specimens was examined by measuring both the critical stress intensity factor and the critical strain energy release rate.
Abstract: Linear elastic fracture mechanics was used to study longitudinal crack propagation in bovine compact bone. The resistance to crack initiation in slotted specimens was examined by measuring both the critical stress intensity factor, K" and the critical strain energy release rate, G,. A change in specimen thickness (from 0.185 to 0.380 em) did not affect the value of K, (or G,). A significant positive correlation (P < 0.01) was found between K, (or G,) and dry density. A companson of the experimentally determined effective modulus (relating K, and G,) with an effective modulus calculated from the transversely isotropic model for bone showed good agreement.
01 Jan 1977
TL;DR: In this article, self-similar pressure profiles in the symmetrically-extending plane crack were discussed and the effects of gas penetration on the energy release rates at the tips of a symmetric extending plane crack.
Abstract: Publisher Summary This chapter discusses self-similar pressure profiles in the symmetrically-extending plane crack. It also discusses the effects of gas penetration on the energy release rates at the tips of a symmetrically extending plane crack. All pressure profiles exert the same opening force on the crack faces because of the stress intensity factor. The extent of gas penetration has a profound effect on the energy release rate. The results can only form a qualitative basis for the equation of motion of a pressurized crack in a blasting situation.
TL;DR: For an elastic perfectly plastic solid containing a crack, the energy release rate G is equal to the plastic dissipation rate p (using Rice's notation), for crack extension at any load, provided the stresses change continuously during crack extension as mentioned in this paper.
Abstract: Recently the writers' attention has been drawn to a paper by Rice [I] in which he showed that, for an elastic perfectly plastic solid containing a crack, the energy release rate G is equal to the plastic dissipation rate p (using Rice's notation), for crack extension at any load, provided the stresses change continuously during crack extension. This result has been used as a criticism of previous work [2,3] by one of us (A.R.L.) in which a surplus surface energy rate Q(= G p) was calculated by a finite element method and used to predict stable cracking in thin aluminium plates.
01 Jun 1977
TL;DR: In this article, the results of an investigation of the strength of cracked steel-fiber-reinforced concrete subjected to a flowing salt water environment were presented. Butler et al. used the plane strain fracture toughness method of testing metallic materials using a modified wedge opening loading (WOL) specimen.
Abstract: : This report presents the results of an investigation of the strength of cracked steel-fiber-reinforced concrete subjected to a flowing salt water environment. The testing procedure was adapted from the plane strain fracture toughness method of testing metallic materials using a modified wedge opening loading (WOL) specimen. Concrete specimens were cast with 1.0, 1.5, and 2.0 percent concentrations of steel fibers by volume of concrete and cured for 28 days in a moisture room. After 28 days, a notch was sawed in each of the specimens with a masonry saw, and a small crack was propagated from the tip of the notch by mechanical means. Control specimens then underwent a compliance testing procedure to determine the work rate necessary to propagate a crack through the specimens. The remaining specimens were subjected to a flowing saltwater environment for four different exposure intervals. The strain energy release rate of the specimens exposed to saltwater was determined and compared with that of the control specimens. The rate of change of strain energy release rate decreased with increasing time and with increasing steel fiber content. (Author)
TL;DR: In this paper, the authors investigated the factors which may influence the formation of shear lips and found that they contribute very much to crack arrest phenomena and are influenced by crack velocity, temperature, constraint (stress triaxiality) and applied stress level in this case.
Abstract: From the viewpoint of energy balance concept, the resistance of material against fast fracture can be measured by the capacity for absorbing energy dissipated due to crack extension. With respect to brittle fracture of steel, energy absorption is associated with the formation of both flat brittle fracture surface and shear lips.In the previous report, stress gradient type double tension tests using mild steel were carried out and it was found that shear lips were able to absorb rather large amount of energy and played an important role to arrest behavior of brittle crack. In order to evaluate the arrestability of steel, it is thus necessary to clarify the mechanism of initiation and growth of shear lips.In this study, experiments are carried out to investigate the factors which may influence the formation of shear lips. Surface-notched double tension specimen using mild steel is adopted. Crack propagates initially in the notched region where shear lips may be restrained, and then propagates into full thickness region where crack may arrest due to fall of driving force and/or shear lip formation.Data obtained are analyzed on the basis of dynamic fracture mechanics. Shear lips contribute very much to crack arrest phenomena and are influenced by crack velocity, temperature, constraint (stress triaxiality) and applied stress level in this case.
01 Jun 1977
TL;DR: In this paper, room-temperature static and cyclic tests were made on 21 aluminum plates in the shape of a 91.4x91.4cm Maltese cross with 45 deg flaws to develop crack growth and fracture toughness data under mixed-mode conditions.
Abstract: Room-temperature static and cyclic tests were made on 21 aluminum plates in the shape of a 91.4x91.4-cm Maltese cross with 45 deg flaws to develop crack growth and fracture toughness data under mixed-mode conditions. During cyclic testing, it was impossible to maintain a high proportion of shear-mode deformation on the crack tips. Cracks either branched or turned. Under static loading, cracks remained straight if shear stress intensity exceeded normal stress intensity. Mixed-mode crack growth rate data compared reasonably well with published single-mode data, and measured crack displacements agreed with the straight and branched crack analyses. Values of critical strain energy release rate at fracture for pure shear were approximately 50% higher than for pure normal opening, and there was a large reduction in normal stress intensity at fracture in the presence of high shear stress intensity. Net section stresses were well into the inelastic range when fracture occurred under high shear on the cracks.