Showing papers on "Stress concentration published in 1971"

An elastic-plastic stress analysis for a notched bar in plane strain bending

Abstract: An elastic-plastic stress analysis, which allows for linear work-hardening, has been carried out for a notched bar using the method of finite elements. Good agreement has been found with available experimental data and confirmation obtained of the idea that the strain at the notch surface is nearly constant over a large fraction of the root. However, some interesting differences exist between the present results and those apparently predicted from slip-line field theory. First, there is the surprising result that the maximum stress does not occur at the elastic-plastic interface. Secondly, in considering the stress intensification (the ratio, R , of the maximum stress to the yield stress), it is shown that slip-line field theory apparently over-estimates R at low loads but slightly under-estimates it near to general yield. The results for the stress intensification are used to re-analyse existing experimental data in order to find the temperature variation of the local fracture stress: this is found to be nearly constant over a range of 250°C.

Fracture mechanics of interfacial cracks

Abstract: This paper contains a two-dimensional analysis of the stress field around a crack on the plane interface between two bonded dissimilar anisotropic elastic half-spaces. This analysis is then combined with the usual local form of the Griffith virtual work argument to give an explicit fracture criterion which involves a suitably defined ‘stress concentration vector’ and the specific surface energy of the bonded surfaces. This criterion has a simple structure and reduces to the conventional form of Irwin when the two half-spaces are isotropic and identical. The analysis is then extended to cracks moving uniformly and a local fracture criterion with the same structure as the static criterion is derived by an energy balance argument. The criterion is specialized to isotropic half-spaces for illustration, when it predicts that the speed of a crack on an interface between such media will be limited by a speed Vc which is slightly greater than the smaller of the two Rayleigh wave speeds. A by-product of the analysis is an expression for the displacement field of an arbitrary interfacial dislocation, either stationary or moving uniformly.

Effect of Width and Length on Stress Intensity Factors of Internally Cracked Plates Under Various Boundary Conditions

Abstract: This paper is concerned with the analysis of stress intensity factors of a strip with a longitudinal crack subject to tension and bending along its edges, and the tension of rectangular plates with a central crack. For both problems three types of boundary conditions, that is, stress conditions, displacement conditions and their combinations are considered. Analysis is based on Laurent expansions of the complex potentials satisfying the stress free relations along the crack. The expansion coefficients are determined from boundary conditions along outer edges, by using a perturbation technique in the first problem and a boundary collocation procedure based on resultant forces and mean displacements in the second problem. Numerical calculations are performed for various plate configurations, and the results are summarized in forms ready for practical use. The accuracy of numerical results are also examined, and they are regarded as correct up to four figures.

The Hertzian fracture test

Abstract: The crack growth in the non-uniform stress field due to the contact loading of a spherical ball on an elastic half-space is described quantitatively for the case of an isotropic brittle solid. This theoretical understanding provides a basis for the Hertzian test which may be used to measure three important surface properties of strong solids and consequently their strength. These are fracture toughness, surface crack size densities and residual stress. All examples of applications of the test are described in detail for glass but the application to a wider variety of strong materials is implied and gives the test a wider significance.

Stress Concentration Factors for Bonded Lap Joints

Abstract: This paper is concerned with the stress analysis by the finite element method of a bonded, single, lap joint. Since the adhesive layer is of primary importance, the stresses occurring in it are presented. A modified version of the well-known Wilson stress analysis program is used for the case of plane stress. The total length beyond the lap is considered long compared to the lap length. Stress concentrations as functions of dimensionless, geometric and material parameters are presented. For a given load (7, the important maximum shearing stress concentration, rmax/(7, and tearing stress concentration

Delay Effects in Fatigue Crack Propagation

Abstract: The fatigue crack propagation behavior resulting from variations in load is examined for 2024-T3 aluminum alloy, from both a macroscopic and a fractographic point of view. A peak load is found to cause retardation of the crack growth rate, which becomes more pronounced as the percentage overload or baseline stress intensity level or both is increased. The delaying effect of the overload is observed to exist for a calculated crack length increment equivalent to the plastic zone size formed during the peak load. Multiple overloads and high-low block loading sequences are found to result in additional retardation. It is observed that the macroscopic fracture surface appearance (that is, transition to plane stress) is a function of the crack growth rate. From fractographic examination it is found that the initiation of microvoid coalescence during fatigue occurs when plane stress conditions are achieved; this limits the extent of the stretch zone associated with an overload cycle. As a result, the stretch zone is found to be followed by striations in plane strain and by dimples under plane stress conditions. The size of the stretch band is observed to depend on the stress intensity level during the overload cycle. The usefulness of closure concepts in aiding the understanding of fatigue crack propagation under uniform and nonuniform loading conditions is considered. Evidence is given to demonstrate the general applicability of closure concepts for analysis of macroscopic and fractographic fatigue crack propagation results. /Author/

Application of fracture mechanics in the analysis of pavement fatigue

Abstract: THE PURPOSE OF THIS PAPER IS TO PREDICT THE FATIGUE LIFE OF PAVING MIXTURES IN TERMS OF MATERIAL CONSTANTS, GEOMETRY, BOUNDARY CONDITIONS, AND THE STATE OF STRESS. FATIGUE IS DEFINED IN TERMS OF CRACK INITIATION, INFLUENCES ON CRACK GROWTH, AND CRITICAL STRESS INTENSITY AT THE CRITICAL FAILURE POINT. CRACK GROWTH PARAMETERS WERE DETERMINED FROM BEAM LOADING EXPERIMENTS. FATIGUE LIFE ESTIMATES BASED ON THESE PARAMETERS AGREED CLOSELY WITH EXPERIMENTALLY DETERMINED VALUES.

New method for the statistical evaluation of constant stress amplitude fatigue-test results

Abstract: REGRESSION MODELS, BASED ON LINEAR ELASTIC FRACTURE MECHANICS, ARE USED TO INTERPRET THE EFFECT OF STRESS RATIO ON FATIGUE CRACK GROWTH RATE IN 7075-T6 ALUMINUM ALLOY. IT IS SHOWN THAT FATIGUE CRACK GROWTH RATE CAN BE RELATED TO RANGE AND MAXIMUM VALUES OF STRESS-INTENSITY FACTOR. STATISTICAL TECHNIQUES ARE USED TO EXAMINE THE ERROR WHICH MAY ACCUMULATE WHEN REGRESSION EQUATIONS ARE USED TO PREDICT CRACK GROWTH VERSUS CYCLES CURVES. /ASTM/

Fatigue Crack Propagation in Polymethylmethacrylate; the Effect of the Mean Value of Stress Intensity Factor

Abstract: Polymeric components often contain structural defects which give rise to regions of internal stress concentration. As the engineering application of these materials expands, the need to understand their behaviour under various loading conditions becomes more necessary.This paper reports the results of part of a programme of research undertaken to study fatigue crack propagation phenomena in thermoplastics.A fracture mechanics approach is used and the effects of the mean stress intensity factor, Km, and the range of stress intensity factor, ΔK, on crack propagation phenomena in polymethylmethacrylate are studied.Based on the experimental data available, a relationship of the following form, between the cyclic crack growth rate d(2a)/dN and the tensile loading levels, has been proposed d(2a)/dN = β(Kmax2 – Kmin2) nwhere Kmax and Kmin are the maximum and minimum values of the stress intensity factor in each loading cycle. In tests at room temperature (21°C), in air, at a loading frequency of 5 Hz, n was foun...

Aspects of Stage II fatigue crack propagation in low-carbon steel

Abstract: The transition from structure sensitive to structure insensitive Stage II fatigue crack propagation, which has recently been observed in carbon steels, has been studied. The transition crack length is determined by the ratio of plastic zone radius at the crack tip to the grain diameter. An explanation of the transition in terms of constraint at the crack tip is suggested. No systematic change in fatigue crack propagation rate is observed with changes in grain size.

Mode II Fatigue Crack Propagation

Abstract: Fatigue crack propagation rates were obtained for 2024-T3 bare aluminum plates subjected to in-plane, mode I, extensional loads and transverse, mode II, bending loads. These results were compared to the results of Iida and Kobayashi for in-plane mode I-mode II extensional loads. The engineering significance of mode I-mode II fatigue crack growth is considered in view of the present results. A fatigue crack growth equation for handling mode I-mode II fatigue crack growth rates from existing mode I data is also discussed.

Elastic Crack Analysis by a Finite Element Hybrid Method

Abstract: The paper presents an efficient finite element method for evaluating the elastic stress intensity factors at the tip of a sharp crack. The method is based on a hybrid stress model for which special stress terms which represent the correct singularity behavior at the crack tip can be included. The magnitudes of such singular terms which are among the unknowns of the final matrix equations are, in fact, the stress intensity factors to be evaluated. Example solutions include plane stress cracks of both the opening type and in-plane shear type for isotropic materials and of the opening type for anisotropic materials. (Author)

Fatigue strength of high-yield reinforcing bars

Abstract: The stress range to which a reinforcing bar is subjected is the primary factor determining its fatigue life. For design purposes, there is a limiting stress range, the fatigue limit, above which a reinforcing bar will have a finite fatigue life and is certain to fracture. At stress ranges below the fatigue limit, a reinforcing bar will have a long fatigue life and may be able to sustain a virtually unlimited number of stress cycles. The magnitude of the fatigue limit depends on the minimum stress during each stress cycle and on the shape of the deformatins rolled onto the bar surface. It may also depend on the diameter and the grade of the bar. Increasing a tensile minimum stress was found to result in a decrease in fatigue strength. On the other hand the fatigue was found to incrase with an increasing compressive minimum stress. Bar diameter and grade of bar were found to influence the finite-life fatigue strength of reinforcing bars. The existence of a long-life fatigue effect due to these variables could not be established. Larger size bars have a lowered fatigue strength while higher grade bars have an increased fatigue strength. The effect of lug geometry on fatigue strength was found to be coupled with that of bar diameter. The larger the bar diameter, the greater was the effect of lug geometry.

The effect of environment on the mechanism of Stage I fatigue fracture

Abstract: Fatigue crack propagation in nickel-base superalloys at low and intermediate temperatures occurs predominantly in the Stage I mode, along {111} slip planes Cracking normally starts at an external surface and the Stage I fracture surface has a cleavage appearance Both of these factors indicate that the environment may play an important role in this mode of propagation To assess the role of environment in Stage I fracture and to determine the mechanism of failure, fatigue tests were run in air and vacuum on single crystals of low-carbon MAR-M200 The fatigue life at room temperature is significantly greater in vacuum than in air, and the improvement in life increases as the stress range is reduced Fatigue crack propagation in specimens tested in air and in vacuum is entirely in the Stage I mode, but only the specimens tested at low stress ranges in air have a cleavage appearance In vacuum and at high applied stress levels in air, fracture surfaces have a matte appearance with fewer fracture steps and river lines At high magnifications, a dimpled structure is observed on these fracture surfaces The fatigue life in air can be attributed to a faster rate of crack growth resulting from oxygen adsorption at the crack tip A model for Stage I fatigue crack propagation in planar slip materials is presented which is an extension of the Griffith-Orowan criterion to cases where localized cleavage occurs at a crack tip in fatigue

Fatigue Fracture in Polyethylene

Abstract: The application of non-classical fracture mechanics to the growth of dynamic fatigue cracks in a visco-elastic solid is discussed. The ideas developed are used to characterize the results of fatigue crack growth measurements on a range of low-density polyethylenes. The results can be expressed in the form [Note: See the image of page 57 for this formatted text]d$c$/d$N$ = B $\scr{J}^{n}$, where d$c$/d$N$ is the growth of the crack each cycle,[Note: See the image of page 57 for this formatted text]$\scr{J}$ is a fracture mechanics parameter and B, n are constants. Most of the materials studied reveal two distinct regions (with differing values of the constants) linked by a transition zone, and corresponding to brittle and ductile crack propagation respectively. The fatigue life of virgin specimens can be predicted from the crack growth characteristics assuming the existence of intrinsic flaws which (when the predictions are matched to actual fatigue data) are found to correspond in size to the polyethylene spherulites.