The effect of specimen thickness on the experimental and finite element characterization of CTOD in extra deep drawn steel sheets

Recent experimental results by us have indicated that the load-drop technique can serve as a valid fracture criterion for predicting elastic-plastic fracture in extra deep drawn (EDD) steel sheets or in predominantly plane stress conditions. The purpose of this investigation is to examine the validity of aJ-integral as a fracture parameter and theJ-CTOD relation for the determination of critical CTOD in predominantly plane stress fracture (CTOD-crack tip opening displacement). Fracture tests were performed and experimental results were generated on fracture behaviour of EDD (0·06%C) steel sheets with CT specimens and using ‘load-drop’ as a fracture criterion. Critical CTOD was determined by using theJ-CTOD relation in addition to several existing techniques. A full 3-D finite element model was formulated to verify the critical load, critical CTOD and plastic-zone size. The critical CTOD was shown to increase with increasing specimen thickness and appeared to be approaching a higher limiting value. The characteristic features of predominantly plane stress fracture or general yielding fracture mechanics are summarized in conclusion     

On the fracture toughness evaluation in weldments of a maraging steel rocket motor case

Fracture toughness of the weld joints of the maraging steel rocket motor case obtained from the limited Compact Tension (CT) specimens are found to be invalid due to the measured crack lengths through the thickness of the specimens exceeding 10% of the initial crack length. This paper proposes an indirect method to evaluate the pre-crack length of the CT specimen from the recorded load versus crack mouth opening displacement data. The Chauvenet’s criterion is applied. After confirming the initial crack size and other validity conditions, the evaluated fracture toughness is designated as the plane-strain fracture toughness (K_IC).     

Constraint-corrected fracture failure criterion based on CTOD/CTOA

In engineering design, a difficulty has always existed in those standard laboratory tests that cannot accurately predict the behavior of large structures like pipelines due to the different constraint levels. At present, extensive work has been done to characterize the constraint effects on fracture toughness by introducing a second parameter, while the systematic research on constrained transformation is inadequate. To address this issue, the ductile fracture process of X65 SENB specimen is simulated through the finite-element method coupled with the Gurson–Tvergaard–Needelman model. The parameters crack tip opening displacement (CTOD) and crack tip opening angle (CTOA) are chosen to characterize the fracture behaviors. The effects of specimen thickness on fracture toughness based on CTOD/CTOA and constraints ahead of crack tips in SENB specimen are studied. The results indicate that the critical values of CTOD/CTOA decrease with the increase of specimen thickness, but the constraint parameters are opposite. Furthermore, it finds that there is a near linear relationship between critical values of CTOD/CTOA and the stress constraint ahead of the crack tip. Thus, a constraint-corrected fracture failure criterion based on CTOD/CTOA is proposed, which can be used for the prediction and simulation of stable tearing crack growth in specimens and structures, made of this steel with any thickness value.     

Paper multilayer with a fracture toughness of steel

We demonstrate in this paper that commercially available printing paper can reach very high fracture toughness, comparable to that of steel, simply due to a special arrangement of the paper sheets with respect to the crack. Fracture mechanics experiments are conducted on single sheets of paper as well as on multilayer specimens in crack divider and crack arrester configuration. It is demonstrated that an arrangement in crack arrester configuration leads to an increase of the fracture toughness by a factor ten. An explanation of the effect is given and the transferability to other materials is discussed.     

Effect of rare-earth treatment on the banded microstructure and fracture properties of a 16 Mn steel

The two treatments, namely rare-earth (RE) additions to the mould and Ca-Si injection into the ladle, were used to control the MnS inclusion shape in a 16 Mn steel. The critical crack opening displacement, δ_c, method and tensile testing were used to determine the fracture properties of the steel sheets. Scanning electron microscope (SEM) fractography of the fracture surface of tensile specimens tested at room temperature clearly showed the banded structure of the steel sheets in all, even modified, steels. The RE treatment improved the fracture properties both by sulphide inclusion shape control and by reducing microstructural heterogeneity.     

Effect of loading rate on dynamic fracture initiation toughness of brittle materials

Numerical simulation is carried out to investigate the effect of loading rate on dynamic fracture initiation toughness including the crack-tip constraint. Finite element analyses are performed for a single edge cracked plate whose crack surface is subjected to uniform pressure with various loading rate. The first three terms in the Williams’ asymptotic series solution is utilized to characterize the crack-tip stress field under dynamic loads. The coefficient of the third term in Williams’ solution, A ₃, was utilized as a crack tip constraint parameter. Numerical results demonstrate that (a) the dynamic crack tip opening stress field is well represented by the three term solution at various loading rate, (b) the loading rate can be reflected by the constraint, and (c) the constraint A ₃ decreases with increasing loading rate. To predict the dynamic fracture initiation toughness, a failure criterion based on the attainment of a critical opening stress at a critical distance ahead of the crack tip is assumed. Using this failure criterion with the constraint parameter, A ₃, fracture initiation toughness is determined and in agreement with available experimental data for Homalite-100 material at various loading rate.     

Thickness effect on the mode III fracture resistance and fracture path of rock using ENDB specimens

Study of the thickness effect in predicting the crack growth behavior and load bearing capacity of rock‐type structures is an important issue for obtaining a relation between the experimental fracture toughness of laboratory subsized samples and the real rock structures with large thickness. The fracture of rock masses or underground rock structures at deep strata may be dominantly governed by the tensile or tear crack growth mechanism. Therefore, in this research, a number of mode I and mode III fracture toughness experiments are conducted on edge notch disc bend (ENDB) specimen made of a kind of marble rock to investigate the effect of specimen thickness on the corresponding K_Ic and K_IIIc values. It is observed that the fracture toughness of both modes I and III are increased by increasing the height of the ENDB specimen. Also, the ratio of K_IIIc/K_Ic obtained from each thickness of the ENDB specimens is compared with those predicted by some fracture criteria, and it was shown that the minimum plastic radius (MPR) criterion is the main suitable criterion for investigating the fracture toughness ratio K_IIIc/K_Ic . Also, the effect of ENDB height on fracture trajectory of tested samples is assessed. It is shown that the crack grows curvilinearly in thicker ENDB samples and cannot extend along the crack front in small specimens.     

The measurements of fracture toughness of ductile materials

Near tip strain is proposed as a ductile fracture criterion. This criterion was used to study the onset of slow growth of surface crack. The data from two batches, B and C, of fully annealed 2024-0 aluminum alloy and HY-80 steel substantiated the proposed criterion. The measured fracture toughness at the onset of surface crack growth are 280, 110 and 800 ksi √in. for these three materials respectively. It was demonstrated that the measurement can be made easily with a small foil resistance strain gage. The near tip strain criterion was compared with both crack surface opening displacement and J-integral criteria.     

Analysis of the effect of biaxial loading on the fracture toughness of reactor pressure-vessel steels

The stress-strain state at the crack tip and its relation to the crack opening displacement and the J-integral under biaxial loading have been studied by solving elastoplastic problems in a geometrically nonlinear formulation by the finite-element method. Numerical investigations have been performed for various cracks and two modes of biaxial loading (tension and bending) under conditions of both small-scale and large-scale yielding. For prediction of the influence of biaxial loading on fracture toughness (at brittle fracture) a procedure has been developed that is based on established laws of stress-strain state formation at the crack tip under biaxial loading and a criterion of brittle fracture proposed earlier. The effect of biaxial loading on fracture toughness is predicted as applied to reactor pressure-vessel steels. Calculated results are compared with avilable experimental data. Alternative approaches to prediction of the effect of biaxial loading on fracture toughness are discussed. TsNII KM “Prometei,” St. Petersburg, Russia. Translated from Problemy Prochnosti, No. 5, pp. 5–26, September–October, 1999.     

Notch root contraction as a fracture measurement

The value of displacement measurements in fracture toughness testing is discussed; in particular the measurement of notch root contraction. The mechanisms of plastic deformation at the notch tip are described, leading to a discussion of theoretical relationship between notch root contraction and crack opening displacement. Experimental work is described in which notched bend specimens of a low alloy steel were loaded to fracture. Each specimen was simultaneously instrumented with notch contraction, COD, and “clip-in” gauges. The equality between notch root contraction and COD was confirmed and observations are made on the relative value of the different measurements. Further observations on the distribution of contraction around the notch tip were made.     

Stress intensity factors as the fracture parameters for delamination crack growth in composite laminates

A “mutual integral” approach is used to calculate the mixed-mode stress intensity factors for a free-edge delamination crack in a laminate under tensile loading conditions. This “mutual integral” approach, for generalized plane strain conditions, is based on the application of the path-independent J integral to a linear combination of three solutions: one, the problem of the laminate to be solved using the quasi 3-D finite element method, the second, an “auxiliary” solution with a known asymptotic singular solution, and the third, the particular solution due to the out-of-plane loading. A comparison with the exact solutions is made to determine the accuracy and efficiency of this numerical method. With this “mutual integral” approach, it was found that the calculated mixed-mode stress intensity factors of the free-edge delamination crack remain relatively constant as the crack propagates into the laminate. It was also found that the fracture criterion based on the mixed-mode stress intensity factors is more consistent with the experimental observations than the criterion based on the total energy release rate, and hence demonstrates the importance of the ability to calculate each individual component of the stress intensity factors. Furthermore, it was found that the fracture toughness measurements from double cantilever beam specimens can be used directly to predict the onset of delamination crack growth between two dissimilar laminae. Using these fracture toughness measurements from the double cantilever beam specimens, some examples are given to show that the fracture criterion based on the mixed-mode stress intensity factors can accurately predict the failure load for various laminates under tensile loading conditions.     

Prediction of the temperature dependence of fracture toughness of 12Cr–2Ni–Mo refractory steel

We study the influence of temperature and the size of the specimens on the characteristics of static crack resistance of 12Cr–2Ni–Mo refractory steel. It is shown that, in the temperature range 20–450°C, the increase in the thickness of specimens leads to an insignificant increase in fracture toughness obtained along a 5% secant line according to the standards of evaluation of the characteristics of crack resistance. The evaluation of the characteristics of crack resistance of 12Cr–2Ni–Mo steel with regard for the scale effect according to an earlier developed numerical-experimental model reveals the existence of satisfactory agreement with the experimental data in the entire investigated temperature range. Translated from Problemy Prochnosti, No. 4, pp. 78–88, July–August, 2009.     

On fracture toughness and its size dependence for steels showing thickness delamination

The effect of thickness delamination on fracture toughness has been studied. The test material used was a martensitic-austenitic pressure vessel steel. Tests were performed on compact tension and three point bend specimens of varying sizes. All specimens were machined from plate material of 100 mm thickness. It was found that the ASTM practice of test evaluation leads to a size dependence of fracture toughness although data for all specimens fulfill the ASTM size requirements. This size dependence has been explained theoretically and it was shown that an evaluation method based on a fixed absolute amount of apparent crack extension would lead to coinciding data for all specimen sizes.     

Static fracture toughness of ultra-fine grained steels processed by thermo-mechanical warm rolling

Ultra-fine grained steels were recently developed by thermo-mechanical warm rolling. Their low-temperature fracture toughness was evaluated in terms of crack tip opening displacement (CTOD) in this paper. Effect of temperature on CTOD and the correlation between CTOD and grain size were investigated, and the experimental results showed that refining ferrite grains can increase the fracture toughness of steel and lower the sensitivity of fracture toughness to temperature. The fracture toughness of the developed ultra-fine grained steels was superior to that of hot-rolled steel SM490B with similar chemical composition.     

A finite fracture mechanics approach to structures with sharp V-notches

Criteria assuming that failure of quasi-brittle materials is affected by the stresses acting over a finite distance from the crack tip are widely used inside the scientific community. For instance, they have been applied to predict the failure load of specimens containing sharp V-notches, assuming as a critical parameter the average stress ahead the notch tip. However, this kind of approaches disregards energy balance considerations, which, as well known, are the basis of linear elastic fracture mechanics (LEFM). In order to overcome these drawbacks, the present paper uses a recently introduced finite fracture mechanics (FFM) criterion, i.e. a fracture criterion assuming that crack grows by finite steps. The length of this finite extension is determined by a condition of consistency of both energy and stress requirements; as a consequence, the crack advancement is not a material constant but a structural parameter. The criterion is applied to structures with sharp V-notches. The expression of the generalized fracture toughness, which is a function of material tensile strength, fracture toughness and notch opening angle, is given analytically. Finally, we provide comparisons with: (i) the experimental data we obtained from testing Polystyrene specimens under three point bending; (ii) some experimental data available in the literature. The agreement between theoretical predictions and experimental results is generally satisfactory and, for most of the cases analyzed, the FFM predictions are better than the ones provided by the simple average stress approach.     

Influence of specimen size and microstructure on the fracture toughness of a martensitic stainless steel

The fracture toughness of alloy HT-9,² a martensitic stainless steel under consideration for fast reactor and fusion reactor applications, was determined from circular compact tension specimens using the multi-specimen R-curve method. Specimens with thicknesses of 11.94, 7.62 and 2.54mm and widths of 23.88 and 11.94 mm were tested to investigate the effects of specimen size on fracture toughness. The test results obtained from all specimens are in good agreement and thickness requirements for a valid J_1c test are satisfied. The experiment indicates that small specimens of HT-9 may be used for post-irradiation fracture toughness testing.Fractographic examination of the fracture surfaces reveals that fracture in HT-9 is significantly influenced by delta ferrite stringers present in the material. The fracture surface examination and crack opening displacement measurements for specimens tested at various temperatures are consistent with the temperature dependence of the J_1c results.     

Plane strain fracture toughness of modern ferritic structural steels

Abstract

The temperature dependence of the plane strain fracture toughness of a low carbon, fine grain, ferritic steel for structural applications is investigated. The ductile–brittle transition is found to occur in the interval between 160 and 184 K. The experimental results are interpreted by an analytical model which permits calculation of the plane strain fracture toughness K _1c in the brittle domain as a function of the tensile properties and the cleavage fracture stress, making use of a piecewise approximation for the distribution of tensile stress on the crack axis and applying a deterministic fracture criterion at the stress peak. A similar criterion, which consists of equating the severest strain on the crack axis to a critical strain for cavity nucleation, provides the upper shelf fracture toughness. A relatively simple figure for predicting the transition temperature of steels in this family as a function of material properties can be obtained in this way.     

Effect of compressive transverse normal stress on mode II fracture toughness in polymeric composites

Effect of transverse normal stress on mode II fracture toughness of unidirectional fiber reinforced composites was studied experimentally in conjunction with finite element analyses. Mode II fracture tests were conducted on the S2/8552 glass/epoxy composite using off-axis specimens with a through thickness crack. The finite element method was employed to perform stress analyses from which mode II fracture toughness was extracted. In the analysis, crack surface contact friction effect was considered. It was found that the transverse normal compressive stress has significant effect on mode II fracture toughness of the composite. Moreover, the fracture toughness measured using the off-axis specimen was found to be quite different from that evaluated using the conventional end notched flexural (ENF) specimen in three-point bending. It was found that mode II fracture toughness cannot be characterized by the crack tip singular shear stress alone; nonsingular stresses ahead of the crack tip appear to have substantial influence on the apparent mode II fracture toughness of the composite.     

Out-of-plane stretching and tearing fracture in ductile sheet materials

Pre-cracked ductile steel sheets are fractured by combined in-plane streching and bending. The deformation mimics the mode of fracture when plating is dented and torn as in ship grounding. Fracture toughness is determined for this mode of tearing. Values are greater than those obtained with DENT testpieces on the same material because of the different mode of crack opening. This revised version was published online in August 2006 with corrections to the Cover Date.     

Determination of fracture toughness from thin side-grooved specimens

Methods of determining fracture toughness from specimens of thickness lower than that required by ASTM Standard, E399 were studied using aluminum and titanium alloy specimens. In thin specimens in which crack growth initiation is clearly marked by a sudden change in the slope of the load-displacement curve, the stress intensity at the crack growth initiation point was found to be the same as the standard fracture toughness value. Crack growth initiation was more easily identifiable in the aluminum alloys than in the titanium alloy, although the latter was more brittle. Side grooves enable identification of crack growth initiation in thinner specimens, reducing considerably the thickness requirement for fracture toughness testing. A nearly straight crack front was found to be essential for obtaining reproducible results. Sharp and deep side grooves produced fatigue cracks leading at the edges.