The transition between stress corrosion crack growth and plastic fracture

The paper focuses on the behaviour of materials for which the onset of crack extension and unstable fracture coincide in a rising load fracture mechanics test. A theoretical analysis shows that use of the experimental test J_Ic value gives a non-conservative prediction of unstable fracture when a stress corrosion crack grows in a solid that is subject to a sustained high stress. Consequently, when an engineering component is to be used at high stress levels in an environment where stress corrosion cracking might be expected, there are clear advantages in having a material which exhibits stable crack growth in a fracture mechanics test.     

Effect of crosshead speed on the fracture toughness of Soda-lime glass, Al2O3 and Si3N4 ceramics determined by the surface crack in flexure (SCF) method

The fracture toughness of soda-lime glass, Al₂O₃ and Si₃N₄ specimens was measured by the surface crack in flexure method. For the soda-lime glass specimens, the fracture toughness was calculated from the initial crack size and flexure strength, and the value increased with increasing crosshead speed. This trend seems to be related to the difficulty in determining the critical crack size at fracture, since slow crack growth occurs during bending test. For the Al₂O₃ specimens, a halo region (stable crack growth region) was formed around the initial precrack during bending test. The halo size increased and the resultant flexure strength decreased with decreasing in the crosshead speed. The halo region, however, could not be observed in the Si₃N₄ specimens. Despite of the difference in the appearance of halo region, the fracture toughness of the Al₂O₃ and Si₃N₄ specimens was constant irrespective of the crosshead speed when the values were calculated with the critical crack sizes at fracture (halo incorporated crack sizes). The constant fracture toughness with the crosshead speed could be explained by the relation between the changes of halo size (thus critical crack size at fracture) and resultant flexure strength.     

Crack tip displacement factor-D: an application to two dimensional linear elastic fracture mechanics

A fracture parameter, crack tip displacement factor D is introduced to characterize the two-dimensional linear elastic fracture mechanics problems. Similar to the conventional COD approach, the D factor can be determined directly from the crack surface displacement. The major advantage of using this fracture control parameter is that one can obtain it by evaluating the crack surface displacement from a numerical analysis or an experiment without the need for considering the stress field at the crack tip. Unlike the COD method, the introduced fracture parameter may be used for not only the simple opening mode but also for the sliding and tearing modes as well as for the mixed mode fracture problems. This article presents a detailed derivation of the D factor as well as some sample applications.     

Determination of Critical Tearing Energy of Tyre Rubber

Abstract:  An experimental investigation was conducted to determine the crack growth characteristics and critical tearing energy of pure tyre rubber under mode-I and -III loading. Constrained tension and trousers specimens were used, respectively. In the trousers test it was observed that the crack does not propagate at a steady rate, but in a stick–slip way, i.e., it is arrested and re-initiated at fairly regular intervals. Thus, the force necessary to propagate the crack varies widely from a maximum value at crack initiation to a minimum value at crack arrest. In the constrained tension tests, no stable crack growth was observed and crack initiation coincides with catastrophic fracture. The critical tearing energies corresponding to crack initiation and arrest under mode-III and to unstable crack growth under mode-I loading were determined from the load–displacement records by an approximate analysis of the trousers and the constrained tension tests.     

A load–deformation formulation with fracture representation based on the J–R curve for tubular joints

This study presents a new fracture formulation to describe the ductile tearing and unstable fracture failure for circular hollow section (CHS) joints under monotonically increasing brace tension. The initiation of the ductile tearing occurs when the crack driving force in an assumed initial shallow crack reaches the material fracture toughness determined from a standard fracture toughness test. The joint behavior prior to the ductile crack initiation follows a previously proposed nonlinear formulation based on the latest strength equations recommended by the International Institute of Welding. The load–deformation characteristics beyond the crack initiation assume that the energy release rate and the amount of crack extension adhere to the experimentally measured J–R curve, prior to the unstable fracture failure. Unstable fracture, which leads to the total loss of the joint capacity, occurs when the crack driving force reaches the maximum fracture resistance determined from the J–R curve test. The proposed load–deformation representation for tubular joints, when implemented in the large-scale K-frame pushover analysis with a material fracture toughness test, predicts successfully the global frame response governed by the joint fracture failure, as observed in the frame test.     

The dependence of the strength of zinc sulphide on temperature and environment

The dependence of the strength of zinc sulphide on temperature, environment, surface finish and specimen size has been assessed. Room-temperature fracture stresses were determined using a bursting disc geometry for a number of different surface finishes and for two different sample sizes. High and low-temperature fracture stresses in a dry nitrogen atmosphere were obtained from experiments using the Brazilian test geometry and showed that the average strength of the material remained above or equal to the room-temperature value within the range –70 to +600 °C. The Brazilian test is an indirect tensile technique which is attractive for its experimental simplicity but gives fracture stress values which are consistently below those obtained by direct tensile techniques. The data from this test were therefore compared at room temperature to results obtained from the bursting disc test on samples which had been prepared using the same techniques. The possibility of delayed failure through environmentally enhanced slow crack growth was evaluated using the double-torsion technique which revealed slow crack growth below the critical stress intensity factor.     

Theoretical and experimental study on unstable fracture for type 304 stainless steel plates with a soft tensile testing machine

The structural materials used for the LWR piping system are mainly stainless steels of Type 304, 316 or similar ones. Because of the very high toughness of these materials, unstable fracture can be usually excluded as a failure mode, and so the leak-bef ore-break concept is generally accepted as a design basis for the LWR piping made of the above materials. However, there have been questions about the fact that the leak-before-break concept can still be established for the LWR piping with very soft loading condition, which may be close to a dead load condition and regarded to be very severe from the point of view of the stability of crack extension. In the actual LWR piping, this kind of loading is deeply related to the length of pipe compared with its other dimensions and also to the character of internal pressure.From the theoretical point of view, the stability of crack growth is recently discussed using the concept of T, the so called tearing modulus. The condition of stability of crack growth is given by the nondimensional squantities T_mat and T_appl, where the former is value of the material resistance curve, and the latter is the “applied” value of T.The object of this paper is to show experimental results on stable as well as unstable fractures for Type 304 stainless steel plates with a central crack using a soft tensile testing machine. The test machine was installed specially for the safety study of nuclear piping systems and its maximum loading capacity and maximum displacement are 600 ton and 500mm, respectively. The compliance of the machine is 1.0 × 10^?4(mm/N).The transition points from the stable to the unstable crack growth observed in the test were theoretically determined by using three methods. In the first method, the “applied” value of T was calculated with the simple expression based on the dimensional analysis. In the second method, the fully-plastic solutions were used to calculate the nonlinear value of J, which was added to the linear value of J, thus the “applied” value of T was determined by differentiating the total value of J, which was obtained for the material with the Ramberg-Osgood type stress-strain relation. In the final method, the finite element method was fully utilized to determine the “applied” value of T. The value of J in the finite element method was obtained with the use of the path-integral.Comparing the calculated transition points from stable to unstable crack growths with the experimental ones for several cases, it was found that the discrepancies between the theoretical and experimental results were within allowable limit.     

Propagation of fatigue cracks from notches

Abstract

The traditional design approaches to fatigue at notches, based on stress level–endurance relationships, are briefly reviewed. It is shown, by considering crack propagation from notches and invoking a change in control mode from notch plasticity to crack-tip plasticity, that a critical stress condition can be obtained which must be exceeded if the crack is to propagate to failure. The traditional techniques are then reinterpreted and explained by this propagation method. An example is given of crack growth from a sharp defect at a weld toe. It is shown that the integration of an elastic fracture mechanics growth law can reproduce stress range–cycles to failure data for this situation. There are, however, complexities of stress analysis and crack shape. A simple treatment of residual stresses affecting the threshold and slow–growth regimes, shows some promise as a technique for accounting for residual stresses.

MST/70     

Damage characterization of a cross-ply carbon fiber/epoxy laminate by an optical measurement of the displacement field

Using Electronic Speckle Pattern Interferometry (ESPI), full-field displacement measurement was performed on the edge of a cracked cross-ply graphite/epoxy laminate subjected to a tensile loading. The displacement jumps corresponding to cracks are clearly visible and can be used to determine the crack opening displacement (COD) values along the cracks. The main objective of this study is to determine if the application of successive loads of increasing magnitude may have modified the existing cracks and thereby changed the COD dependence on the applied stress. Moreover, we have tested the applicability of the assumed linear elastic COD behavior in the presence of very high stress concentration at the crack tips. The profile of the opening along the crack was also studied.     

Analysis of incremental cracking by the stress-wave emission technique

One of the most fruitful areas for application of the acoustic emission technique lies in characterization of yielding and fracture processes. For example, what are the microscopic details of the macroscopic slow crack growth process that precedes crack instability? Fundamental to answering this is the ability to detect and quantify the microcracking phenomena. It was found that the emission of a single elastic stress wave could be correlated to a load drop, ΔP, occuring during crack growth. Furthermore, this load drop could be interpreted via a theoretical compliance analysis in terms of area swept out by the advancing crack. It is proposed that any discrete stress wave emission associated with a fracture process can be interpreted in terms of an incremental fracture area, ΔA. This is given by

$\text{g=}\text{2·5 m K W}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{δA}\text{YLB}$

where g is the amplitude of the emission. K is the applied stress intensity, L is the distance between grips, W is the specimen width, B is the specimen thickness. Y is f(a/w) and m is the proportionality constant between stress wave amplitude and $\text{ΔP}\text{B}$. Crack-line loaded or compact tension specimens of 7075-T6 aluminum were used for the experimental investigation. A theoretical relationship between the load drop and the crack growth step was derived for this test specimen configuration. Over fifty experimental observations verified the linear relationship between g and $\text{ΔP}\text{B}$. For the above relationship, m was found to be 0.05 in²/lb sec² from the compact tension data.     

Threshold toughness of polymers in the ductile to brittle transition region by different approaches

The fracture behavior of polymers in the ductile-to-brittle region is neither completely brittle nor entirely ductile. Besides, scatter in toughness results impairs the situation. Consequently, conventional methods based exclusively either on linear elastic fracture mechanics theory (LEFM) or on non-linear elastic fracture mechanics theory (NLEFM) are not suitable. It was demonstrated previously, that Weibull statistical method could be successfully used to determine the toughness threshold of polymers displaying ductile-to-brittle behavior. The present study compares the threshold toughness value determined by the statistical approach with other critical values calculated following other different suitable approaches: Low temperature plane strain fracture toughness, Plastic zone corrected fracture toughness, Stable and unstable propagation combined model, J extrapolated at zero stable propagation value, and Quasi J-R curve. The analysis was carried out on data points taken from fracture tests performed on polypropylene homopolymer, PPH, and on a blend of PPH and an elastomeric polyolefin, PPH/POes. The results of this analysis indicate that statistical, stable and unstable propagation combined model, and the J extrapolated at zero stable propagation value methods yield to very similar toughness threshold values being practically equivalent. In this case, threshold value was slightly smaller than the minimum J displayed by the experimental replicas, suggesting that it is an actual representative material toughness. Among these methodologies, the Statistical Method is applicable even if stable crack growth is difficult to determine. On the other hand, the methodologies based on LEFM tended to underestimate the fracture toughness, being very conservative while Quasi J-R curve method based on NLEFM overestimated the PPH/POes toughness value.     

Crack initiation from a sharp notch and stretched zone

The “crack tip COD” at the fracture initiation mainly consists of the stretched zone, the new surface which appeared due to the slip deformation at the notch tip. Therefore, the COD or the stretched zone width at the fracture initiation is a very important parameter which reflects the notch tip behavior until fracture initiation.In the case of fibrous crack initiation, the stretched zone width ($\text{S}{}_{\mathrm{i}}$) and COD ($\text{δ}{}_{\mathrm{i}}$), where $\text{δ}{}_{\mathrm{i}}$ ≈ √2 $\text{S}{}_{\mathrm{i}}$, take almost constant values regardless of temperature, specimen geometry, preloading (if the total $\text{δ}{}_{\mathrm{i}}$ is taken), slit angle (in the case of mixed mode condition) and so on, while, in the case of cleavage fracture initiation, COD and the stretched zone width take various values between the value at the fibrous crack initiation ($\text{δ}{}_{\mathrm{i}}$ or $\text{S}{}_{\mathrm{i}}$) and almost zero, depending on temperature and plastic constraint.     

Estimation and comparative study of JIC using different methods for 20MnMoNi55 steel

Fracture toughness is one of the key input variables to compute critical load of the structural components. The resistance against ductile fracture can be quantified either by the initiation value or by the entire resistance curve. Different standard methods like J_SZW, JSME and ASTM: E1820 etc. are mainly used to estimate the critical crack initiation value from the resistance curve developed by the J-integral test. However, the results vary from method to method and are even inconsistent for the same method. Pehrson and Landes suggested a simple method for estimation of the critical fracture toughness by identifying the critical point corresponding to the maximum load on load–displacement curve. In the present study, different standard methods along with the one suggested by Pehrson and Landes are used to find out the critical fracture toughness using 1T–CT and ½T–CT specimens of the material 20MnMoNi55 steel for varying temperatures and crack size. The results are analyzed to compare the merits of the different methods of estimation of fracture toughness.     

The transition between stress corrosion crack growth and plastic fracture—II. The effect of loading pattern

The paper addresses the problem of predicting the onset of plastic fracture at the tip of a growing stress corrosion crack, using data from laboratory fracture mechanics tests. A theoretical analysis for a particular model: namely that of the place strain deformation of a solid with two symmetrically situated deep cracks, and with tension of the small remaining ligament, shows that plastic fracture occurs at a $\text{J}$ value that is not constant, but depends on whether the loading is load or displacement control. This result, which is valid for materials for which the onset of crack extension and unstable fracture are coincident in a rising load fracture mechanics test, provides valuable support for the view that great care must be exercised when using fracture mechanics procedures to predict the transition between stress corrosion crack growth and plastic fracture in such materials.     

Stability of a system of interacting cracks

In the absence of crack branching, a system of straight cracks may interact and their growth regime may become unstable in the sense that some cracks may grow faster at a certain critical state, or even snap into a longer length, while other cracks may stop growing, or even snap closed.When the crack extension involves Modes I, II, and III, and the fracture criterion is defined by a critical value for the total energy release rate, necessary and sufficient conditions are developed for both the stability of a given regime, and for unstable crack growth.     

Microstructure and mixed mode I/II fracture of AA2524-T351 base material and friction stir welds

Mixed mode I/II experiments for base material AA2524 indicate that (a) transition from a local opening mode of fracture to a local shear mode of fracture occurs in AA2524 at much lower levels of far-field shear loading than observed in AA2024, showing the increased potential for mode transition in the cleaner aluminum alloy AA2524 and (b) the measured critical crack opening displacement (∣COD_crit∣) in AA2524 is isotropic and equal to the maximum measured value (LT orientation) in AA2024.Mixed mode I/II experiments in AA2524 friction stir weld specimens show that (a) changes in microstructure and particularly, reduction in constituent particle volume fraction result in virtual elimination of fracture along constituent particle bands, (b) AA2524 has an increased tendency to transition from local mode I to local mode II crack growth during stable tearing and (c) specific features observed during the fracture process (e.g. mode transition) are shown to be directly correlated to both metallurgical differences in the FSW microstructure and local variations in the measured COD_crit.     

Temperature effects on quasi-static fracture of PMMA

The effect of temperature on the quasi-static fracture behaviour of PMMA is examined. It is found that the critical stress intensity factor, K ₁₀, at crack growth initiation decreases with temperature up to a certain critical temperature, T _c. Above T _c, K ₁₀ increases rapidly. The speeds with which slow crack growth could be maintained without transition to brittle fracture were found to be significantly higher at high temperatures.     

Nature of scatter of fracture toughness in static loading

The previously proposed model of unstable fatigue crack growth is used to explain a large (in comparison with other mechanical characteristics) scatter of static fracture toughness for 15Kh2MFA and 15Kh2NMFA steels at temperatures below the tactile-brittle transition temperature. The results show that for the materials for which K_fc ¹ < K_Ic the critical stress intensity factor K_Ic depends on the specific energy of inelastic strain W at the tip of the initial fatigue crack in its formation stage. The value of W is a function of the number of load cycles (in the conditions with a constant range of the stress intensity factor K) as a result of irregular fatigue crack growth. Here K_fc ¹ is the minimum cyclic fracture toughness. A method is proposed of evaluating the minimum fracture toughness of the material in static loading based on inspection of the process of irregular fatigue crack growth in the stage of crack initiation.Translated from Problemy Prochnosti, No. 2, pp. 10–16, February, 1990.     

The effects of ferrrite grain size on fracture of low carbon steel under mixed modes I and II

In the previous article a new methodology is proposed for the study on fracture criterion for the notched or cracked specimens under mixed Modes I and II. In this methodology, any value of K_II/K_I can be applied to the thin-walled hollow cylindrical specimen with notch or crack, the length of which is perpendicular to the specimen axis. Thus the data can be obtained covering all values of K_II/K_I ranging from ∝ to 0, that is, from mode II to mode I.Using this method, the experimental studies were carried out on the effects of ferrite grain diameter upon the fracture of low carbon steel under mixed Modes I and II. The experimental results were compared with various fracture criteria hitherto proposed in literatures. The fracture criterion experimentally obtained is a function of ferrite grain diameter and the value of K_II/K_I, at fracture increases with increase of ferrite grain diameter. On the other hand, the overall direction of the crack growth obeys approximately maximum stress criterion or energy momentum tensor criterion, independent of ferrite grain diameter. Furthermore, this also shows that the fracture criterion does not reveal directly overall direction of crack growth. These characteristics are quite similar in trend to those of the unnotched specimens.     

Evaluation of crack growth behavior and probabilistic S–N characteristics of carburized Cr–Mn–Si steel with multiple failure modes

The unexpected failures of case-hardened steels in long life regime have been a critical issue in modern engineering design. In this study, the failure behavior of a carburized Cr–Mn–Si steel under very high cycle fatigue (VHCF) was investigated, and a model for evaluating the probabilistic S–N curve associated with multiple failure modes was developed. Results show that the carburized Cr–Mn–Si steel exhibits three failure modes including the surface flaw-induced failure, the interior inclusion-induced failure without the fine granular area (FGA) and the interior inclusion-induced failure with the FGA. As the predominant failure mode in the VHCF regime, the interior failure process can be divided into four stages: (i) the small crack growth around the inclusion, (ii) the stable macroscopic crack growth outside the FGA, (iii) the unstable crack growth outside the fish-eye and (iv) the momentary fracture outside the final crack growth zone. The threshold values are successively evaluated to be 2.33 MPa m^1/2, 4.13 MPa m^1/2, 18.51 MPa m^1/2 and 29.26 MPa m^1/2. The distribution characteristics of the test data in transition failure region can be well characterized by the mixed two-parameter Weibull distribution function. The developed probabilistic S–N curve model is in good agreement with the test data with multiple failure modes. Although the result is somewhat conservative in the VHCF regime, it is acceptable for safety considerations.