Low cycle fatigue crack growth prediction for stainless steel. The crack growth rate behaviour with respect to the alternating stress intensity can be explained in different regimes see, figure 1 as follows regime a. Slow crack growth in ceramics is attributed to corrosion assisted stress at crack tips or at any defect preexisting in the ceramic. Conversion for stress intensity factors set both units and the input value on the left hand side. As the stress intensity factor reaches the k ic value, unstable fracture. It has been shown for many materials that the stress intensity factor, k, controls fatigue crack propagation via the cyclic stress intensity range. Why kstress intensity factor has a peculiar unit mpa. The stress intensity factor describes the stress state at a crack tip, is related to the rate of crack growth, and is used to establish failure criteria due to fracture. Crack growth rate an overview sciencedirect topics. The crack grows until it reaches a critical size and failure occurs. This represents the effective local stress at the crack tip. In fracture mechanics, a stress intensity factor is calculated as a function of applied stress, crack size, and part geometry. Fatigue crack growth results raw data from the 23 fatigue crack growth tests may be found in the appendix of this report.
The resulting relationships can then be used in the stripyield model in nasgro stripy, afgrow, or used to generate the stressintensity factor range. Introduction experimental testing for baseline fatigue crack growth rate properties has traditionally been performed on laboratory coupons designed to promote modei crack growth, where cracking is perpendicular to the applied load. Parameters used for characterizing fracture behavior that are derived in the framework of fracture mechanics are. It is characterized by the stress intensity factor. K \displaystyle k characterises the load around a crack tip and the rate of crack growth is experimentally shown to be a function of the range of stress intensity. It is to be emphasized that the current approach is little. Crack tip stress dependence on the stress intensity factor k s y x w xy v yy v xx m u y r a s s s 3 yy 2 k x v s 2 yy 2 k x v s k 1 crack growth rate associated with a specific stress intensity factor. Irwin arrived at the definition of \k\ as a near crack tip approximation to westergaards complete solution for the stress field surrounding a crack 2. As the crack grows the stress intensity factor increases, leading to. The different residual stress distributions have been used analytically. Various fracture criteria and crack growth rules are studied. Threshold stress intensity factor and crack growth rate.
To make life estimations for fatigue crack growth and damage tolerant design, the following information are often needed. The stress intensity factor k or its equivalent partner the elastic energy release rate g, the jintegral, the cracktip opening displacement ctod, and the cracktip opening angle ctoa are the most important parameters used in fracture mechanics. Thiscritical stress intensity factor isthenameasureof. Characteristic stress intensity factor correlations of fatigue crack.
N2 a new mixedmode threshold stress intensity factor is developed using a critical planebased multiaxial fatigue theory and the kitagawa diagram. In this study, k res is calculated using the analytic weight function method wfm and the polynomial distribution of residual stresses. This critical stress intensity factor is then a measure of. Recall that the stress intensity factor is a function of geometry and applied stress. Computation of stress intensity factor and critical crack. Stress intensity factors, crack profiles, and fatigue crack. Stress intensity factor equations for branched crack growth. The stress intensity, k i, represents the level of stress at the tip of the crack and the fracture toughness, k ic, is the highest value of stress intensity that a material under very specific planestrain conditions that a material can withstand without fracture. Paris law is a crack growth equation that gives the rate of growth of a fatigue crack. Mishra evaluation of mixed mode stress intensity factors for interface cracks using efgm applied mathematical modeling 35. Slow crack growth is most suitably described in a v crack velocity versus k i stress intensity factor diagram. K 0 was chosen to yield crack growth rates in the range of 2.
An evaluation of the fatigue crack growth and fracture. Computer controlled decreasing stress intensity technique for. It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion for brittle materials, and is a critical technique in the discipline of. K th is the threshold sif and a and m are the conventional tensile crack growth rate parameters for the given material. Figure 9 is a plot of the fatigue crack growth rate, dadn, as a function of the stress intensity factor range, ak, for the data at the three stress ratios studied in the cr orientation. In order to calculate the stress intensity factor sif of crack tips in twodimensional cracks from the viewpoint of strain energy density, a procedure to use the strain energy density factor to calculate the sif is proposed. Constant amplitude crack growth technical background. The crack growth rate for this example was calculated using a spreadsheet that is augmented by a plug in that performs the stress intensity factor calculations. The crack growth rates of small cracks correlated well with range of the strain intensify factor. It was concluded that the strain intensity factor is valid for predicting the crack growth rate because the fatigue life was correlated well with the strain range and was almost equivalent to cycles for a small crack growing to critical size. Peak stress intensity factor governs crack propagation. Finite element method analysis of stress intensity factor in. This study attempts to analyze the stress intensity factor in various edge cracks along the length of a finite plate which is under a uniform tension. The physical significance of their units is easily understandable like, energy per unit area or energy rate per unit area of crack growth.
Set all four units and the input values of c and n where dadncdkn or. Engineers are interested in the maximum stress near the crack tip and whether it exceeds the fracture toughness. The stress intensity factor, is used in fracture mechanics to predict the stress state stress intensity near the tip of a crack or notch caused by a remote load or residual stresses. It is considered to be a material constant, and in. Calculation of stress intensity factor in twodimensional. The reason for this acceleration in growth is that the growth rate is dependent on the stress intensity factor at the crack tip, and the stress intensity factor is dependent on the crack size, a. An analytical model for the identification of the threshold.
Failure occurs once the stress intensity factor exceeds the materials fracture toughness. The application of such results in crack growth rate prediction is addressed. Fatigue crack growth rate and stressintensity factor. Paris law also known as the pariserdogan equation is a crack growth equation that gives the rate of growth of a fatigue crack. The linear portion of the curve represents stable crack growth and is characterized by an intercept, c, and slope, m. The value of the stress intensity factor sif range threshold for fatigue crack growth fcg depends highly on its experimental identification. Rather than deal with giant stress concentrations, fracture mechanics uses a stress intensity factor, k. So, a straightline segment will result when logdadn versus log k data are plotted. The stress intensity factor k \displaystyle k k characterises the load around. Nomenclature a crack length, or half length for a symmetric crack. Dotfaaar0749 analyses of fatigue crack growth databases. The stress intensity factor, k \displaystyle k k, is used in fracture mechanics to predict the stress state stress intensity near the tip of a crack or notch caused.
Subject terms dmmge tolerance, fracture mechanics, crack initiation, toughness, stress intensity factor, residual strength, crack propagation, fatigue, inspection. I want to find the material constant c, m and kth of high. Volume i1 treats exclusively the subject of damage tolerance evaluation of airframes 14. The combined presence of body fluid molecules mainly water, which reduce the surface energy at. You have to conduct the fatigue crack growth rate fcgr experiments, plot the crack growth rate dadn vs stress intensity factor range delk to get these numbers. Lets say we have within a structural member an elliptical hole of major axis 2a with radius of curvat. The crack growth rate accelerates as the maximum stress intensity factor approaches the fracture toughness of the material. The authors have devised an approach for correcting both the crack growth rates and stress intensity factors based on twodimensional mixed modeiii finite element analysis fea.
Crack growth analysis requires a crack growth curve for the material. The crack growth rate and the stress intensity factor are measured independently and a permanent autographic test record is produced from which the crack growth rate and the stress intensity conditions can be verified at any time. First consider a conventional strength of materials approach. Thus, the stress intensity factor k is commonly expressed in terms of the applied stresses at and. Unit conversion issues related to fracture mechanics quantities. Fatigue crack propagation rate logarithm crack growth rate versus logarithm stress intensity factor range for a nimov steel. As the crack grows the stress intensity factor increases, leading to faster growth. Fracture mechanics materials technology eindhoven university. The slope and intercept correspond to the values of m and log a, respectively.
At low growth rates, variations in microstructure, mean stress or load ratio, and environment have significant effects on the crack propagation rates. Finite element method is utilized for the analysis. Threshold intensity factors as lower boundaries for crack. The rate at which a crack grows depends on both stress range and crack. Paris 6 that there is a region of stable crack growth for which there is a relationship between the fatigue crack growth rate, dadn mm.
Stress intensity article about stress intensity by the free. In welded joint, the residual stresses effect can be considered using the residual stress intensity factor k res. At high stress intensities, crack growth rates are extremely high and little fatigue life is involved. The stress intensity factor is calculated for a given geometry and load, and compared with a threshold value of k above which cracks will propagate in the given material. Stress intensity factors are presented for various geometries with residual stress fields.
K is computed from the applied stresses and crack length. Domarkas stanford university stanford, california 94305 abstract the reflection coefficient of a rayleigh wave at a surface crack is measured in both the long wave. T1 threshold stress intensity factor and crack growth rate prediction under mixedmode loading. The identification and application of are not well established as its determination depends on various factors including experimental, numerical, or analytical techniques used. It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion for brittle materials. At this point the crack will grow in a rapid and unstable manner until fracture. The nonlinear, crack surface overlapping effect is noted, and the case of cracks emanating from notches in residual stress fields is shown to be an associated problem.
775 485 1293 866 699 97 1173 787 1031 288 1167 758 458 136 1083 472 1318 1211 1062 1198 1250 265 1452 807 329 103 25 1486 512 1491 1274 451 778 559 562 334 1465 1463 442