Showing papers on "Fracture mechanics published in 1991"

Fatigue of materials

Abstract: Preface 1. Introduction and overview Part I. Cyclic Deformation and Fatigue Crack Initiation: 2. Cyclic deformation in ductile single crystals 3. Cyclic deformation in polycrystalline ductile solids 4. Fatigue crack initiation in ductile solids 5. Cyclic deformation and crack initiation in brittle solids 6. Cyclic deformation and crack initiation in noncrystalline solids Part II. Total-Life Approaches: 7. Stress-life approach 8. Strain-life approach Part III. Damage-Tolerant Approach: 9. Fracture mechanics and its implications for fatigue 10. Fatigue crack growth in ductile solids 11. Fatigue crack growth in brittle solids 12. Fatigue crack growth in noncrystalline solids Part IV. Advanced Topics: 13. Contact fatigue: sliding, rolling and fretting 14. Retardation and transients in fatigue crack growth 15. Small fatigue cracks 16. Environmental interactions: corrosion-fatigue and creep-fatigue Appendix References Indexes.

Mixed mode cracking in layered materials

Abstract: Publisher Summary This chapter describes the mixed mode cracking in layered materials. There is ample experimental evidence that cracks in brittle, isotropic, homogeneous materials propagate such that pure mode I conditions are maintained at the crack tip. An unloaded crack subsequently subject to a combination of modes I and II will initiate growth by kinking in such a direction that the advancing tip is in mode I. The chapter also elaborates some of the basic results on the characterization of crack tip fields and on the specification of interface toughness. The competition between crack advance within the interface and kinking out of the interface depends on the relative toughness of the interface to that of the adjoining material. The interface stress intensity factors play precisely the same role as their counterparts in elastic fracture mechanics for homogeneous, isotropic solids. When an interface between a bimaterial system is actually a very thin layer of a third phase, the details of the cracking morphology in the thin interface layer can also play a role in determining the mixed mode toughness. The elasticity solutions for cracks in multilayers are also elaborated.

Family of crack-tip fields characterized by a triaxiality parameter—I. Structure of fields

Abstract: Central to the J-based fracture mechanics approach is the existence of a HRR near-tip field which dominates the actual field over size scales comparable to those over which the micro-separation processes are active. There is now general agreement that the applicability of the J-approach is limited to so-called high-constraint crack geometries. We review the J-annulus concept and then develop the idea of a J-Q annulus. Within the J-Q annulus, the full range of high- and low-triaxiality fields are shown to be members of a family of solutions parameterized by Q when distances are measured in terms of J σ 0 , where σ0 is the yield stress. The stress distribution and the maximum stress depend on Q alone while J sets the size scale over which large stresses and strains develop. Full-field solutions show that the Q-family of fields exists near the crack tip of different crack geometries at large-scale yielding. The Q-family provides a framework for quantifying the evolution of constraint as plastic flow progresses from small-scale yielding to fully yielded conditions, and the limiting (steady-state) constraint when it exist. The Q value of a crack geometry can be used to rank its constraint, thus giving a precise meaning to the term crack-tip constraints, a term which is widely used in the fracture literature but has heretofore been unquantified. A two-parameter fracture mechanics approach for tensile mode crack tip states in which the fracture toughness and the resistance curve depend on Q, i. JC(Q) and JR(Δa, Q), is proposed.

Quasi-static fault growth and shear fracture energy in granite

Abstract: The failure process in a brittle granite sample can be stabilized by controlling axial stress to maintain a constant rate of acoustic emission. As a result, the post-failure stress curve can be followed quasi-statically, extending to hours the fault growth process which normally would occur violently in a fraction of a second. Using a procedure originally developed to locate earthquakes, acoustic emission arrival-time data are inverted to obtain three-dimensional locations of microseisms. These locations provide a detailed view of fracture nucleation and growth.

Crack propagation in b.c.c. crystals studied with a combined finite-element and atomistic model

Abstract: A new method for combined finite-element and atomistic analysis of crystal defects has been developed. The coupling between the atomistic core and the surrounding continuum is described in terms of non-local elasticity theory. Static and dynamic tests demonstrate the satisfactory performance of this method. The model is applied to crack propagation on cleavage and non-cleavage planes in b.c.c. crystals, using potentials for iron and tungsten as examples. On the cleavage planes, pronounced directions of ‘easy’ crack propagation, besides less favourable directions, are found. On the preferred cleavage plane {100}, easy propagation is possible in any macroscopic direction by microscopic facetting of the crack front into easy directions, while on the secondary cleavage plane {110}, there is only one macroscopic direction in which cracks will propagate easily. On all other planes studied here, plastic processes at the crack tip (twinning and/or dislocation emission) intervene before brittle crack prop...

Aspects of fracture in particulate reinforced metal matrix composites

Abstract: The tensile deformation and fracture behaviour of the aluminium alloy 6061 reinforced with SiC has been investigated. In the T4 temper plastic deformation occurs throughout the gauge length and the extent of SiC particle cracking increases with increasing strain. In the T6 temper strain becomes localised and particle cracking is more concentrated close to the fracture. The elastic modulus decreases with increasing particle damage and this allows a damage parameter to be identified. The fraction of SiC particles which fracture is less than 5%, and over most of the strain range the damage controlling the tensile ductility can be recovered, indicating that other factors, in addition to particle cracking are important in influencing tensile ductility. It is suggested that macroscopic fracture is initiated by the SiC particle clusters that are present in these composites as a result of the processing. The matrix within the clusters is subjected to high levels of triaxial stress due to elastic misfit and the constraints exerted on the matrix by the surrounding particles. Final fracture is then produced by crack propagation through the matrix between the clusters.

A Comparison of the J -lntegral and CTOD Parameters for Short Crack Specimen Testing

Abstract: This study investigates the applicability of the J-integral test procedure to test short crack specimens in the temperature region below the initiation of ductile tearing where J 1 c cannot be measured. The current J-integral test procedure is restricted to determining the initiation of ductile tearing and requires that no specimen demonstrates brittle cleavage fracture. The J 1 c test specimen is also limited to crack-depth to specimen-width ratios (a/W) between 0.50 and 0.75. In contrast, the crack tip opening displacement (CTOD) test procedure can be used for testing throughout the entire temperature-toughness transition region from brittle to fully ductile behavior. Also, extensive research is being conducted to extend the CTOD test procedure to the testing of short crack specimens (alW ratios of approximately 0.15). The CTOD and J-integral fracture parameters are compared both analytically and experimentally using square (cross-section) three-point bend specimens of A36 steel with a/W ratios of 0.50 (deep crack) and 0.15 (short crack). Three-dimensional elastic-plastic finite element analyses are conducted on both the deep crack and the short crack specimens. The measured J-integral and CTOD results are compared at various levels of linear-elastic and elastic-plastic behavior. Experimental testing is conducted throughout the lower shelf and lower transition regions where stable crack growth does not occur. Very good agreement exists between the analytical and experimental results for both the short crack and deep crack specimens. Results of this study show that both the J-integral and the CTOD fracture parameters work well for testing in the lower shelf and lower transition regions where stable crack growth does not occur. A linear relationship is shown to exist between J-integral and CTOD throughout these regions for both the short and the deep crack specimens. These observations support the consideration to extend the J-integral test procedure into the temperature region of brittle fracture rather than limiting it to J 1 c at the initiation of ductile tearing. Also, analyzing short crack three-point bend specimen (a/W < 0.15) records using the load versus load-line displacement (LLD) record has great potential as an experimental technique. The problems of accurately measuring the CMOD of short crack specimens in the laboratory without affecting the crack tip behavior may be eliminated using the J-integral test procedure.

Instability in dynamic fracture

Abstract: Cracks in brittle materials have terminal velocities far below theoretical predictions. To address this problem we have investigated the propagation of cracks in a brittle plastic (polymethylmethacrylate). Velocity measurements with resolution an order of magnitude better than past experiments reveal the existence of a critical velocity at which the velocity begins to oscillate, the mean acceleration drops sharply, and a pattern is formed on the fracture surface. Thus the dynamics of cracks may be governed by a dynamical instability.

Weight Functions and Stress Intensity Factor Solutions

Abstract: Hardbound An important element of work in fracture mechanics is the stress intensity factor - the characterizing parameter for the crack tip field in a linear elastic material; something reflected in its intense research over the last 30 years The weight function method is one of the most reliable, versatile, and cost-effective methods of evaluating the stress intensity factors and crack opening displacements This book provides a valuable account of the author's research in these fields It has two aims: firstly to provide a theoretical background to the weight function method in fracture mechanics for accurate analysis of two-dimensional crack problems; and secondly, to provide a significant number of stress intensity factor solutions for practical cases The result is an easy-to-use, accurate analytical method for analysing crack problems, an ideal reference source for graduate students, researchers, and engineers involved with the fracture and fatig

Size effect on diagonal shear failure of beams without stirrups

Abstract: The paper presents the results of recent tests on diagonal shear failure of reinforced concrete beams without stirrups. The results indicate a significant size effect and show a good agreement with Bazant's law for size effect. Scatter of the test results is much lower than that previously found by studying extensive test data from the literature, which have not been obtained on geometrically similar beams. The tests also show that preventing bond slip of the longituudinal bars causes an increase of the brittleness number of the beam. It is concluded that the current design approach, which is intended to provide safety against the diagonal crack initiation load, should be replaced or supplemented by a design approach based on the ultimate load, in which a size effect of the fracture mechanics type, due to release of stored energy must be taken into account.

A molecular interpretation of the toughness of glassy polymers

Abstract: A model is proposed that describes the failure of glassy polymers in the crazing regime. This model is based on the realization that the cross-tie fibrils, which are known to exist between primary fibrils in all crazes, can have a profound effect on the failure mechanics of a craze as they can transfer stress between the broken and unbroken fibrils. A very simple model of crack tip stress amplification caused by the cross-ties is shown to work well in the prediction of the fracture toughness of a bulk, high molecular weight, glassy polymer

A framework to correlate a/W ratio effects on elastic-plastic fracture toughness (J c )

Abstract: Single edge-notched bend (SENB) specimens containing shallow cracks (a/W < 0.2) are commonly employed for fracture testing of ferritic materials in the lower-transition region where extensive plasticity (but no significant ductile crack growth) precedes unstable fracture. Critical J-values Jc) for shallow crack specimens are significantly larger (factor of 2–3) than the Jc)-values for corresponding deep crack specimens at identical temperatures. The increase of fracture toughness arises from the loss of constraint that occurs when the gross plastic zones of bending impinge on the otherwise autonomous crack-tip plastic zones. Consequently, SENB specimens with small and large a/W ratios loaded to the same J-value have markedly different crack-tip stresses under large-scale plasticity. Detailed, plane-strain finite-element analyses and a local stress-based criterion for cleavage fracture are combined to establish specimen size requirements (deformation limits) for testing in the transition region which assure a single parameter characterization of the crack-tip stress field. Moreover, these analyses provide a framework to correlate Jc)-values with a/W ratio once the deformation limits are exceeded. The correlation procedure is shown to remove the geometry dependence of fracture toughness values for an A36 steel in the transition region across a/W ratios and to reduce the scatter of toughness values for nominally identical specimens.

Size Effect in Fatigue Fracture of Concrete

Abstract: Crack growth caused by load repetitions in geometrically similar notched concrete specimens of various sizes is measured by means of the compliance method. It is found that the Paris law, which states that the crack length increment per cycle is a power function of the stress intensity factor amplitude, is valid only for one specimen size (the law parameters being adjusted for that size) or asymptotically, for very large specimens. To obtain a general law, the Paris law is combined with size-effect law for fracture under monotonic loading, proposed previously by Bazant. This leads to a size-adjusted Paris law, which gives the crack length increment per cycle as a power function of the amplitude of size-adjusted stress intensity factor. The crack growth is also characterized in terms of the nominal stress amplitude.

Essential work of fracture and j‐integral measurements for ductile polymers

Abstract: In the ductile tearing of polymers that neck before failure it is shown that the specific essential fracture work (we), consisting of the energies dissipated in forming and tearing the neck, is a material property for a given sheet thickness and is independent of specimen geometry. Work of fracture experiments using both double deep-edge notched (DENT) and deep-center notched tension (DCNT) geometries with different ligament lengths yielded almost identical we values for a grade of high-density polyethylene. These measurements for we are in fairly good agreement with the theoretical values based on the J integral evaluated along a contour surrounding the neck region near the crack tip. Under J-controlled crack growth conditions, it is shown that Jc obtained by extrapolation of the JR curve to zero crack growth and the slope dJ/da are identical, respectively, to we and 4βwp obtained from the straight line relationship between the specific total work of fracture (wf) and ligament length (l).

Hydrogen-induced strain localization and failure of austenitic stainless steels at high hydrogen concentrations

Abstract: Mechanical behavior and fractography of hydrogen-austenitic stainless steelsolid solutions were studied to determine the microstructural origins of hydrogen-assisted fracture. AISI 310S and 304 stainless steels containing hydrogen in homogeneous solid solution in concentrations up to approximately 15 at.% resulted in an increase in flow stress by more than a factor two. The loss in ductility increased with increasing hydrogen content and was accompanied by an increasing frequency of “brittle” secondary cracks. The 304 alloy was embrittled at lower concentrations than was the 310S. In the polycrystalline austenitic stainless steels “brittlw” cracking was predominantly intergranular, although there was evidence of shear crack formation along operating slip planes. Intensely localized shear along active slip planes was found on both fracture surface and on polished side surfaces on specimens containing solute hydrogen. Shear localization in the hydrogen-austenitic stainless steel solid solutions appeared to result from the limitation of the number of active slip systems by increasing the local stress to operate dislocation sources. In this study there was no evidence that hydrogen lowered the strength of internal interfaces, rather fracture was found to result from an extreme localization of slip into narrow slip bands and increased difficulty in slip transfer across interfaces.

Fracture mechanics and cavitation in rubber-like solids

Abstract: Conditions for propagation of a pressurized crack within a rubber-like solid are derived in terms of the elastic properties of rubber, the fracture energyGc and the initial radiusro of the crack. A previously proposed criterion, that the critical internal pressurePc for crack growth is given by 5E/6, whereE is the tensile (Young) modulus of elasticity, is shown to be inadequate both for small cracks, when the stiffening of rubber at high strains must be taken into account, and for large cracks, when the critical degree of inflation is so small that the assumptions leading toPc=5E/6 do not apply. However, this simple criterion is found to remain a useful guide for cracks having initial radii lying in an intermediate range, such thatroE/Gc lies between about 0.0005 and 1. For representative rubber-like solids, this corresponds to the rangero=0.5 μm to 1 mm.

Kinking of a Crack out of an Interface: Role of In‐Plane Stress

Abstract: A crack lying in the interface between two brittle elastic solids can advance either by continued growth in the interface or by kinking out of the interface into one of the adjoining materials. This competition can be assessed by comparing the ratio of the energy release rates for interface cracking and for kinking out of the interface to the ratio of interface toughness to substrate toughness. The stress parallel to the interface, σ0, influences the energy release rate of the kinked crack and can significantly alter the conditions for interface cracking over substrate cracking if sufficiently large. This paper provides the dependence of the energy release rate ratio on the in-plane stress. The nondimensional stress parameter which emerges is, σ0(a/E* Ti)1/2, where a is the initial length of the kink into the substrate, E* is a modulus quantity, and Ti is the fracture energy of the interface. An experimental observation of the cracking of reaction product layers in bonds between Ti(Ta) and Al2O3 is rationalized by the theory.

Mechanics of Dynamic Debonding

Abstract: Singular fields around a crack running dynamically along the interface between two anisotropic substrates are examined Emphasis is placed on extending an established framework for interface fracture mechanics to include rapidly applied loads, fast crack propagation and strain rate dependent material response For a crack running at non-uniform speed, the crack tip behaviour is governed by an instantaneous steady-state, two-dimensional singularity This simplifies the problem, rendering the Stroh techniques applicable In general, the singularity oscillates, similar to quasistatic cracks The oscillation index is infinite when the crack runs at the Rayleigh wave speed of the more compliant material, suggesting a large contact zone may exist behind the crack tip at high speeds In contrast to a crack in homogeneous materials, an interface crack has a finite energy factor at the lower Rayleigh wave speed Singular fields are presented for isotropic bimaterials, so are the key quantities for orthotropic bimaterials Implications on crack branching and substrate cracking are discussed Dynamic stress intensity factors for anisotropic bimaterials are solved for several basic steady state configurations, including the Yoffe, Gol'dshtein and Dugdale problems Under time-independent loading, the dynamic stress intensity factor can be factorized into its equilibrium counterpart and the universal functions of crack speed

A three-dimensional analysis of crack trapping and bridging by tough particles

Abstract: The toughness of a brittle material may be substantially improved by adding small quantities of tough particles to the solid. Three mechanisms may be responsible. Firstly, the front of a crack propagating through the solid can be trapped by the particles, causing it to bow out between them. Secondly, the particles may remain intact in the wake of the crack, thereby pinning its faces and reducing the crack tip stress intensity factors. Finally, the toughness may be enhanced by frictional energy dissipation as particles are pulled out in the wake of the crack. This paper estimates the improvement in toughness that might be expected due to these mechanisms, by means of a three-dimensional model. The analysis considers a semi-infinite crack propagating through a brittle matrix material, which contains a regular distribution of tough particles. Particles in the wake of the crack are modelled by finding an appropriate distribution of point forces that pin the crack faces; and the effect of the crack bowing between obstacles is included by means of an incremental perturbation method based on work byRice [J. Appl. Mech.56, 619 (1985)]. The calculation predicts the shape of the crack as it propagates through the solid; the resulting R-curve behaviour; and the length of the bridged zone in the wake of the crack.

On the temperature distribution at the vicinity of dynamically propagating cracks in 4340 steel

Abstract: T he heat generated due to plastic deformation at the tip of a dynamically propagating crack in a metal causes a large local temperature increase at the crack tip which is expected to affect the selection of failure modes during dynamic fracture and to thus influence the fracture toughness of the material. The distribution of temperature at the tips of dynamically propagating cracks in two heat treatments of AISI 4340 carbon steel was investigated experimentally using an array of eight high speed indium antimonide, infrared detectors. Experiments were performed on wedge loaded, compact tension specimens with initially blunted cracks, producing crack speeds ranging from 1900 to 730 m/s. The measurements provide the spatial distribution of temperature increase near the crack tip on the specimen surface. Temperature increases were as high as 465° C over ambient and the region of intense heating (greater than 100° C temperature rise) covered approximately one third of the active plastic zone on the specimen surface. The observed temperature increase profiles clearly show the three-dimensional nature of the fracture process near the specimen surface and provide valuable information regarding the dynamic formation of shear lips and their role in the dissipation of energy during dynamic crack growth. Preliminary temperature measurements performed on side-grooved specimens are also reported.

The load separation criterion and methodology in ductile fracture mechanics

Abstract: The objective of this paper is to investigate the implications of the load separation criterion for evaluating ductile fracture mechanics parameters. This criterion allows the load to be represented as the multiplication of two separate functions; a material deformation function and a crack geometry function. Load separation implies a method for J-integral evaluating using only a single load-displacement record. The original method for evaluating J, proposed by Begley and Landes, used the energy rate interpretation of Rice which requires several load-displacement records for identical specimens with varying crack lengths. A method based on load separation introduced a new parameter η, ηel and ηpl which greatly simplified J calculation. This parameter which can be a function of geometrical factors is generally evaluated experimentally using the energy rate interpretation of J. In this paper the load separation criterion is used to imply a simple method for evaluating η experimentally. Using blunt notched specimen load versus load point displacement results from the literature, four different configurations with a wide range of stationary crack lengths are evaluated. Also included are several different materials varying from low work hardening to high work hardening. The data include thin and thick sections so that both plane stress and plane strain conditions are evaluated. A new method for η-estimation derived from the implication of the load separation is proposed. This method avoids most of the errors that accumulate in the classical methods of estimation. Both the separation method and the energy rate method are evaluated by comparing the techniques and the results. The results show some new trends in ηpl results for the different configurations evaluated in this paper.

A coherent gradient sensor for crack tip deformation measurements: analysis and experimental results

Abstract: A first order diffraction analysis of an optical interferometer, Coherent Gradient Sensor (CGS), for measuring surface gradients is presented. Its applicability in the field of fracture mechanics is demonstrated by quantitatively measuring the gradients of out-of-plane displacements around a crack tip in a three point bent fracture specimen under static loading. This method has potential for the study of deformation fields near a quasi-statically or dynamically growing crack.