Showing papers on "Fracture mechanics 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.

Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements

Abstract: Triangular and prismatic quadratic isoparametric elements, formed by collapsing one side and placing the mid-side node near the crack tip at the quarter point, are shown to embody the (1/√r) singularity of elastic fracture mechanics and the (1/r) singularity of perfect plasticity. The procedure of performing the fracture analysis for the case of small scale yielding is discussed, and the finite element results are compared with theoretical results. The proposed elements have wide application in the fracture analysis of structures where ductile fracture is investigated. They permit a determination of the relationship between crack tip field parameters, loading, and geometry. And for a given fracture criterion can be applied to the prediction of fracture in structures such as pressure vessels under in service conditions.

A model for crack initiation in elastic/plastic indentation fields

Abstract: A model is proposed for the initiation of microfracture beneath sharp indenters. Using a simple approximation for the tensile stress distribution in the elastic/plastic indentation field, in conjunction with the principle of geometrical similarity, fracture mechanics procedures are applied to determine critical conditions for the growth of penny-like “median cracks” from sub-surface flaws. The analysis provides a functional relationship between the size of the critical flaw and the indentation load necessary to make this flaw extend. Initiation is well defined (unstable) only if the critical flaw lies within a certain size range; outside this range, large flaws can extend stably but small flaws can not extend at all. No flaws can extend below a characteristic minimum load, values of the indentation variables at this load accordingly providing useful threshold parameters. These quantities involve the intrinsic deformation/fracture parameters, hardness and toughness, in a fundamental way, thereby establishing a basis for materials selection in fracture-sensitive applications.

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.

Stress corrosion theory of crack propagation with applications to geophysics

Abstract: The theory of stress corrosion for slow crack propagation is reviewed in the light of classical Griffith theory of fracture. Experimental data for stress corrosion cracking for glasses, ceramics, and metals are reviewed. We suggest that stress corrosion cracking plays an important role in the intrusion of magmas and in the transport of magmas upward through the lithosphere. It is shown that the effect of decreasing temperature (at progressively shallower levels along the geotherm) would be to decrease the crack velocity by several orders of magnitude if other factors were equal. We also propose that stress corrosion may be an important process in time-dependent earthquake phenomena such as premonitory behavior and earthquake aftershocks. We suggest that slow cracking in the earth is not seismically detectable but may nevertheless precede the terminal (catastrophic) phase of the fracture that is discerned as an earthquake. The seismically quiet periods before some earthquakes and the seismically quiet regions beneath some volcanoes may in fact be regimes of slow crack propagation. Slow crack propagation in a lithospheric plate may provide access routes for magmas which give rise to prominent linear volcanic chains.

A numerical study of two-dimensional spontaneous rupture propagation

Abstract: Summary We present a numerical technique to determine the displacement and stress fields due to propagation of two-dimensional shear cracks in an infinite, homogeneous medium which is linearly elastic everywhere off the crack plane. Starting from the representation theorem, an integral equation for the displacements inside the crack is found. This integral equation is solved by a method proposed by Hamano for various initial and boundary conditions on the crack surface. We verified the accuracy of our numerical method by comparing it with the analytical solution of Kostrov, and the numerical solution of Madariaga. A critical stress jump across the tip of a crack (between a grid-point inside the crack and a neighbouring point out-side the crack) is used as our fracture criterion. We find that our critical stress jump is the finite difference approximation to the critical stress-intensity factor used in Irwin's fracture criterion. For an in-plane shear crack starting from the Griffin critical length and controlled by the above fracture criterion, the propagation velocity of the crack-tip is found to be sub-Rayleigh or super-shear depending on the strength of the material (given by the critical stress jump) and the instantaneous length of the crack. In fact, the crack-tip velocity may even reach the P-wave velocity for low-strength materials. Additionally we find that once the crack starts propagating, it accelerates rapidly to its terminal velocity, and that the average rupture velocity over an entire length of fault cannot be much smaller than the terminal velocity, for smooth rupture propagation.

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.

Mechanisms of hydrogen induced delayed cracking in hydride forming materials

Abstract: Mechanisms which have been formulated to describe delayed hydrogen cracking in hydride-forming metals are reviewed and discussed. Particular emphasis is placed on the commercial alloy Zr-2.5 pct Nb (Cb) which is extensively used in nuclear reactor core components. A quantitative model for hydrogen cracking in this material is presented and compared with available experimental data. The kinetics of crack propagation are controlled by the growth of hydrides at the stressed crack tip by the diffusive ingress of hydrogen into this region. The driving force for the diffusion flux is provided by the local stress gradient which interacts with both hydrogen atoms in solution and hydrogen atoms being dissolved and reprecipitated at the crack tip. The model is developed using concepts of elastoplastic fracture mechanics. Stage I crack growth is controlled by hydrides growing in the elastic stress gradient, while Stage II is controlled by hydride growth in the plastic zone at the crack tip. Recent experimental observations are presented which indicate that the process occurs in an intermittent fashion; hydride clusters accumulate at the crack tip followed by unstable crack advance and subsequent crack arrest in repeated cycles.

Influence of microstructure on near-threshold fatigue-crack propagation in ultra-high strength steel

Abstract: Fatigue crack propagation behaviour of an ultra-high strength, silicon-modified AISI 4340 alloy steel (300-M) has been investigated in moist air over an extremely wide range of growth rates from 10−8 to 10−1 mm/cycle. Particular emphasis has been devoted to the influence of microstructure on fatigue-fracture behaviour near the threshold stress intensity, ∆K 0 below which crack growth cannot be detected. By varying microstructure through quench and tempering and isothermal transformations, the threshold stress intensity and near-threshold crack-propagation rates are observed to be influenced by mean stress (load ratio), material strength, grain size, and impurity segregation. The threshold ∆K 0 for crack propagation is found to be inversely related to the strength of the steel, and a relationship between ∆K 0 and cyclic yield stress is observed. It is shown how near-threshold crack -growth resistance can be improved by (i) cyclic softening, (ii) coarsening the prior austenite grain size, and (iii) ...

Analysis and testing of adhesive bonds

Abstract: An adhesive fracture mechanics approach is described with reference to the identification and design of the best tests for evaluating a given adhesive, the definition of the most meaningful fundamental parameters by which adhesives might be characterized, and the application of these parameters to the design of joints and to the prediction of their performance. Topics include standard adhesive test techniques, the theory of adhesive fracture, and adhesive fracture energy tests. Analytical methods and computer techniques for adhesive bonding, chemical and physical aspects of adhesive fracture, and specific applications and aspects of adhesive fracture mechanics are discussed.

Rapid calculation of stress intensity factors

Abstract: A method for computing stress intensity factors for cracks embedded in structural details is described. It consists of adding to accepted solutions for cracks in finite plates and bodies of uniform contour a geometry correction factor which accounts for the stress gradient produced by the geometric discontinuity of the detail. This correction factor is determined by integrating away the stresses normal to the line where the crack is to be inserted. The method is applied to the case of a crack emanating from a circular hole in a plate, and the results are found to be in good agreement with Bowie's numerical solution. Values of the stress intensity factor for cracks emanating from spherical weld porosities, and part-through cracks at stiffeners and cover plate ends are computed.

Sub-critical crack extension and crack resistance in polycrystalline alumina

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.

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.

Near-threshold fatigue crack propagation in ultra-high strength steel: influence of load ratio and cyclic strength

Abstract: Fatigue crack propagation behavior of an ultra-high strength steel (300-M) has been investigated in humid air over a very wide spectrum of growth rates from 10/sup -8/ to 10/sup -1/ mm/cycle. Particular emphasis has been devoted to the influence of mean stress (or load ratio R = K/sub min//K/sub max/) and microstructure on fatigue crack growth near the threshold stress intensity for crack propagation, ..delta..K/sub 0/. Increasing the load ratio from R = 0.05 to 0.70 was found to lead to increased near-threshold growth rates, and a decrease in the threshold stress intensity. Similarly, increasing material strength, by varying the microstructure through quench and tempering and isothermal transformation, resulted in higher near-threshold growth rates, and a marked reduction of ..delta..K/sub 0/. These effects are contrasted with behavior at higher growth rates. The infuence of strength on ..delta..K/sub 0/ is rationalized in terms of the cyclic hardening or softening response of the material, and hence it is shown that cyclic softening can be beneficial to fatigue crack propagation resistance at very low growth rates. The results are discussed in the light of crack closure and environmental contributions to fatigue crack growth at low stress intensities.

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.

The use of the C∗ parameter in predicting creep crack propagation rates:

Abstract: The applicability of the C∗ parameter for the prediction of creep crack propagation rates is considered. A new method for estimating C∗ is presented, the results from which show good agreement with those from an existing technique. Experimental results from creep crack growth tests, conducted on a 1 Cr Mo V steel using both compact tension and single edge notch bend specimens, indicate that good correlation with C∗ is obtained once the effects of stress redistribution become negligible. Finally, comparisons are drawn between C∗ and other possible correlating parameters, and the limitations of each approach are discussed.

Strength Degradation of Glass Resulting from Impact with Spheres

Abstract: The nature and extent of degradation incurred by glass surfaces impacted with spheres of steel and tungsten carbide were studied. The residual strength after impact depends on the velocity, radius, and density of the projectile; on the toughness and (indirectly) the hardness of the target; and, to a lesser degree, on the preexisting mechanical condition of the surface. The damage morphology involves modification of the basic Hertzian cone crack pattern by median (radial) cracks and crushed glass at the impact site. The essential features of the degradation may be predicted by a theoretical analysis of residual strength as a function of impact velocity as derived from indentation fracture mechanics. This study accounts, in particular, for a threshold velocity for significant strength loss, above which further strength decrease is relatively slight. Small, but significant, discrepancies between observed and predicted degradation characteristics are attributed to the departure from ideal Hertzian fracture geometry and to the dynamic nature of the contact. However, it is suggested that quasi-statically based theory may be used for estimating the strength of structural ceramics in small-particle impact situations.

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.

Effect of Grinding on Flaw Geometry and Fracture of Glass

Abstract: Fracture mechanics is combined with fracture surface analysis to analyze brittle failure of glass bars which were tested relative to the direction of grinding. Grinding essentially produces two sets of flaws from which failure occurs. In the most severe set, formed basically parallel to the grinding direction, the ratio of the average depth (a) to the half-width (b) is 0.5. In the less severe set, formed perpendicular to the grinding direction, the average a/b ratio is 1.6. In both sets the most severe flaws are generally associated with a particularly deep grinding groove or gouge. The strength reduction resulting from testing perpendicular to the grinding direction results from the larger flaw size and slightly higher stress-intensity factor resulting from the greater ellipticity of the flaws formed parallel to the grinding grooves and perpendicular to the tensile axis. Detailed analysis of these 2 sets of flaws causing failure of appropriately oriented specimens shows that (1) the fracture mirror radius, r, occurs at a constant stress-intensity level independent of flaw geometry; (2) unsymmetric fracture mirrors result from unsymmetric, irregular flaws leading to unsymmetric stress-intensity distributions; (3) is constant for semielliptical flaws; and (4) fracture energy calculated from an expression including mirror constants, the flaw-to-mirror size ratio, and the flaw geometry agrees with measured values over a wide range of a/b values.