Principle and method for determining fracture toughness of structural steel by side-cut se (B)

In this paper, the principle and method for determining fracture toughness indexes K_IC, δ_C and J_IC of structural steel by side-cut SE (B) are introduced. This method has many advantages: clear critical point, simple operation, stable date, less cost and will be valuable to use more frequently.     

Exploring the fracture toughness KIE and KIC of a medium-Strength steel plate using the surface-flaw test

The fracture toughness of a 30 CrMnSiA steel plate of three thicknesses (10,8 and 5 mm) and three widths (110,80 and 56 mm) has been investigated by using surface-flaw method under room temperature. It is not easy to compute the value of K_IE by the maximum applied load. But the values of K_IE and K_IC could be obtained easily, if the computation of the conditional applied load P₁₀ and P₅ based on the relative effective extension Δa/a₀ = 10% and 5% were adopted, together with the conditions of P_max/P₁₀ 1.2 and P_max/P₅ 1.3. The K_R — Δ_a curve, i.e. the resistance-curve described by the parameter K, has been plotted. The values of K_IC and K_IE are then the resistances corresponding to the real extensions of flaws of Δ/a₀ = 2 and 7%, respectively. These values so obtained are in good agreement with the computed values of K_IC and K_IE by using the conditional applied loads. The values of K_IC and K_IE so obtained are also in agreement with the value of K_IC converted from the J-integral and the effective value of K_IE computed by the maximum applied load, respectively.

An approximate relation between K_IC and K_IE has been found to be: K_IC = (0.85˜0.95)K_IE.

The requirements for the dimensions of specimens are: Thickness of plate: B 1.0(K_IC/σ_0.2)² or 1.25(K_ICσ_0.2)²]; Width of plate: 8 W/B 10, 4 W/2c 5; Effective length: l 2W.     

A comparison on the effect of the ratio a/w on the fracture behaviour between ductile and brittle materials

The effect of the ratio a/W on the fracture behaviour of ductile and brittle materials has been studied by measuring the crack-opening displacement and J-integral for ductile material and the stress intensity factor for brittle material in three-point bend specimens with shallow and deep notches. It is shown that, for ductile material, the values of δ_i and J_i, for specimens with shallow notches are larger than those of deep notches. On the contrary, for brittle material, the values of K_IC for specimens with shallow notches are smaller than those of deep notches. The reason for this is explained.     

Evaluation and analysis of interlaminar fracture toughness of bead filled matrix hybrid composite materials using orthotropic fracture mechanics

Evaluation of Mode I interlaminar fracture toughness for unidirectional hybrid composites fabricated with a bead filled epoxies was carried out. The two important fracture toughness parameters, G_IC and K_IC values of hybrid composites, were reviewed in accordance with the orthotropic fracture model. The deviation of measured G_IC and K_IC values from predicted values were explained based on the critical review of the basic assumption of orthotropic fracture model and characteristic material properties of hybrid composites. It can be said that, basically, the orthotropic fracture model can be used for evaluation of hybrid composite materials. However, careful analysis for G_IC and K_IC values which were derived from different source and some correction factor for K_IC values are necessary.     

Fracture toughness of turbine-generator rotor forgings

A comprehensive program is being conducted relative to applying fracture mechanics technology to large turbine-generator rotors. One facet of this program involves the determination of plane-strain fracture toughness (K_Ic) over a range of temperatures for various types of rotor steels. Data have been obtained for ten large production forgings, representing three alloys, using various types of compact K_IC and spin burst test specimens. These results demonstrate that valid K_IC data can be obtained in these types of intermediate-strength, high-toughness steels in the temperature range of practical interest. Data indicate that the plane-strain fracture toughness of these steels increases rapidly with increasing temperature and is rather high (K_tc/σ_YS > 1 in^1/2), in the application range. As a result, the critical defect sizes for catastrophic failure upon a single cycle of loading are relatively large. The plane-strain fracture toughness measurements, as well as the application of these data, are presented and discussed.     

Influence of specimen size and configuration on the plastic zone size, toughness and crack growth

The main purpose of this investigation is to evaluate the effect of the thickness, width, aspect ratio and geometry of the fracture toughness specimen on the resultant displacement due to growth of plastic zone and crack.

The analytical part evaluates the effect of the width, aspect ratio, geometry and flow properties on the displacement due to the growth of plastic zone as well as the crack. The experimental part evaluates the effect of thickness and width of a compact tension specimen on the displacement and on the thickness direction contraction due to the growth of the plastic zone.

The main result of the investigation is that the plastic zone size decreases and the constraint to yielding increases as the width of a CT specimen increases. Based on this and other analytical and experimental result, a new procedure for the determination of K_IC has been proposed. The procedure is verified by experimental data obtained by other workers. The procedure overcomes the limitation of ASTM E399 for the determination of K_IC.     

Fracture parameters determination at yield point and fracture initiation in instrumented impact testing

A method of fracture parameters determination at yield point and fracture initiation is derived from theoretical analysis of bending load-time response of materials during CHARPY impact testing. It allows to overcome the difficulties due to inertial effect and specimen vibrations. Furthermore, the method enables to determine the time at which fracture initiates, that is when the specimen crack begins to extend. The procedure has been applied to various model materials such as steel, aluminum alloy, PMMA and soda-lime glass in order to specify the fracture parameters which can be carried out by the method. Depending on the type of materials K_id and J_Id can be determined.     

An equivalent domain integral method for three-dimensional mixed-mode fracture problems

A general formulation of the equivalent domain integral (EDI) method for mixed-mode fracture problems in cracked solids is presented. The method is discussed in the context of a 3-D finite-element analysis. The J-integral consists of two parts: the volume integral of the crack front potential over a torus enclosing the crack front and the crack surface integral due to the crack front potential plus the crack-face loading. In mixed-mode crack problems the total J-integral is split into J_I, J_II, and J_III, representing the severity of the crack front in three modes of deformation. The direct and decomposition methods are used to separate the modes. These two methods were applied to several mixed-mode fracture problems in isotropic materials. Several pure and mixed-mode fracture problems were analyzed and results found to agree well with those available in the literature. The method lends itself to be used as a post-processing subroutine in a general purpose finite-element program.     

Application of instrumented impact testing for studying dynamic fracture behaviour of rotor steels

The viability of the instrumented Charpy impact testing for studying dynamic fracture behaviour of rotor steels is investigated. This encompasses determination of dynamic fracture toughness (K_Id) and dynamic J-integral (J_Id), establishing correlation between oscilloscope profiles and fracture morphology of the ruptured samples and identifying fracture mechanisms involved. The predicted oscilloscope profiles for common fracture modes, their experimental counterparts, and the inferences drawn from these concerning operating fracture mechanisms are in good accord with the fractographic observations made on broken samples. Thus, the respective oscillographs vividly manifest the observed variations in the fracture processes. Fracture mechanics analysis of load-time and energy-time records of pre-cracked Charpy samples gave dynamic fracture toughness (K_Id) values of 43, 74 and 124MN/m3/2, and dynamic J-integral (J_Id) values of 0.008, 0.03 and 0.06 MJ/m² at −180°, 26° and 96°C respectively. It is possible that the deduced J_Id values correspond to a small but finite amount of crack extension instead of Zero Crack extension, in line with the emerging trends of J_Id estimation. Apart from increasing with temperature, both parameters recorded a true transition around 35°C which is attributed to the combined influence of a change in the fracture mode and relaxation of crack tip constraint. Another significant outcome of this investigation concerns about the existence of a minimum crack depth ratio for valid J_Id determination which, based on a detailed fractographic study, is interpreted in terms of the collective influence of crack tip plasticity and notch constraint.     

Comparison of fracture toughness test procedures for aluminum alloys

The Dynamic Tear (DT) test permits the measurement of fracture propagation energy across the toughness spectrum for metals which are definable by linear elastic analyses to those requiring gross plastic strains for fracture. The linear elastic fracture mechanics parameter K_ic provides a relationship between critical flaw size and stress level at which crack instability will occur. Unlike the DT test, the K_ic toughness test cannot be utilized for fracture under conditions of elastic-plastic or gross plastic strain.

A correlation has been developed between the DT test and the K_IC parameter for ahuminum alloys. The relationship may also be expressed in terms of β_ic-DT and _ic-DT. The K_ic values were determined with several specimen types and a comparison of the values for different specimens is provided.

The correspondence between K_ic and DT serves several purposes. It provides a frame of reference for DT values obtained from frangible metals that fracture under linear elastic conditions. Accordingly, it permits utilization of the inexpensive DT test to approximate the flaw size-stress instability conditions which otherwise must be determined by the more expensive K_ic test. Furthermore, through extrapolation, it is possible to utilize the DT test to estimate the critical flaw size under an elastic-plastic strain field.     

Studies on fracture toughness and fractographic features in Fe---Mn base alloys

Fractographic examinations of fracture surfaces of single edge crack plate tension fracture toughness test specimens of some new Fe---Mn base maraging alloys have been conducted. The interrelations between the fractographic features, fracture toughness and other mechanical properties of these alloys have been studied. It is observed that the width of the stretched zone between fatigue and rapid fracture is related to K/σ_ys of the material where K is either K_IC, K_Q or the stress intensity for onset of microscopic slow crack growth. The stretched zone width is approximately equal to the average dimple size. Also it is of the order of the process zone size (calculated by modified Krafft's model) and the critical crack opening displacement in plane strain condition. Hahn and Rosenfield's model to estimate K_Ic was found to show much higher values in those cases where the fracture mode was predominantly cleavage, quasicleavage or intergranular.     

Effects of crack growth on the load-displacement characteristics of precracked specimens under bending

A critical evaluation of the feasibility of obtaining crack growth parameters from quasi-static bend tests is presented. First derived are the governing differential equations which characterize the time-history of bend test parameters for a given elastic material exhibiting power law crack growth behavior v = v_max(K_I/K_IC)^N. A numerical solution scheme is then developed which is capable of solving the initial value problem, thus quantitatively assessing the influence of crack growth on the load-displacement output. The results of this analysis indicate that in order to calculateK_IC accurately based on the peak load data, the loading rate has to be set sufficiently fast compared to v_max (but below dynamic rates), otherwise, it will generally overestimate its true value whenever slow crack growth occurs during the test; and that for high N materials the flexural test method gives a broad error band inN prediction and hence is not a reliable technique. However, it can be used by a designer to quickly screen the new materials with high Nvalues which are potential candidates for structural application.     

Theoretical and experimental study of superimposed fracture modes I, II and III

The authors wish to present an all-fracture mode specimen with which it is possible to conduct fracture mechanics tests for pure mode I, pure mode II, pure mode III, as well as for all possible combinations of the above-mentioned. By means of a finite element analysis of this specimen, the stress intensity factors K_I, K_II, and K_III were computed. It was discovered that K_II and K_III are coupled for in-plane shear and anti-plane shear loading, i.e. a mixed state occurs locally. The integral mean along the crack front yields however only to a K_II factor for in-plane shear and to a K_III factor for anti-plane shear loading. Fracture experiments under mixed-mode loading, using this new specimen, demonstrate the influence of the loading type on the orientation and on the structure of the fracture surface.     

On the influence of microstructure on crack propagation mechanisms and fracture toughness of metallic materials

A survey is given on the effect of microstructure on crack propagation mechanisms and fracture toughness.

The influence of inclusions and of the material's matrix are treated separately. An attempt was made to correlate some simple, but typical microstructures with corresponding crack propagation mechanisms and to establish a qualitative sequence of these microstructures with respect to their effect on K_IC. Because of the lack of sufficient experimental evidence this attempt is necessarily incomplete.

Finally, some K_IC-calculations are compared with measured values.     

The scatter in KIC-results

Scatter in K_IC-results can often be quite extensive, and to make reliable interpretations of the results it is of great importance to understand the nature of it. Cleavage fracture in steels is of a statistical nature and therefore the scatter in K_IC-results will behave similarly.

Two different approaches, one based on a microstructural statistical model and an other based on the Weibull distribution are applied to evaluate the theoretical scatter in K_IC-results. With both methods it is shown that the theoretical value of the relative scatter described through the Weibull slope factor is constant and equal to four.

The reason for the discrepancy between the theoretical value and the experimentally determined values of the slope factor is shown to be caused by inadequate number of experimental K_IC-measurements. The existence of a lower limiting K_min value is verified and a simple procedure for conservative estimation of the K_Ic-mean and lower bound values is presented.     

Review of the fracture mechanics approach to creep crack growth in structural alloys

The application of the fracture mechanics approach to time-dependent high temperature crack growth has been reviewed. Available data on several structural alloys indicate that depending on the environmental sensitivity and creep ductility of the material, creep crack growth can be characterized by either linear elastic parameter, K, non-linear elastic-plastic parameter, J^*-integral, or reference stress, σ_ref. In particular for materials that are significantly sensitive to environment, K can adequately characterize the growth rate, and for materials that are significantly creep ductile, σ_ref can be used to predict creep life of a cracked body. Finally, for materials that are relatively ductile and wherein crack growth occurs predominantly by a deformation process, J^* integral appears to be the characterizing parameter for the growth rate. Data for several materials indicate that under steady state crack growth conditions, there may be a unique growth rate-J^* relation independent of temperature and material. This would have a profound impact in terms of the utility of fracture mechanics approach to predict creep crack growth rate and needs to be examined further. Conditions under which K, J^* or σ_ref is applicable are discussed in detail.     

Bridging law and toughness characterisation of CSM and SMC composites

This work presents an experimental investigation of the fracture properties of three different short-fiber-reinforced composites [one chopped strand mat (CSM) and two sheet molding compound (SMC) materials]. Fracture tests are performed on double-cantilever beam (DCB) specimens loaded with pure bending moments. In this experimental configuration, the bridging law for the material can be derived directly from measurements. No significant dependency on specimen height was observed in our results. The bridging laws determined can, therefore, be considered as material properties. The coupling between microstructure and fracture behaviour is discussed through the measured bridging laws. The beneficial effect (in terms of fracture energy) of increasing tendency for pull-out is confirmed for one SMC, referred to as Flex-SMC, which shows remarkably high fracture energy, J_c=56.0 kJ/m², compared to a standard SMC, termed Std-SMC, J_c=25.9 kJ/m². This increasing tendency for pull-out is observed to shift the bridging law towards larger crack openings. On the basis of our observations we find the concept of characterising the failure behaviour in terms of bridging laws attractive since it can be used as a tool for the tailoring of the microstructure towards desired fracture behaviour.     

Effect of stress triaxiality levels in crack tip regions on the characteristics of void growth and fracture criteria

The behaviour of void growth in the crack tip regions of four specimen geometries with different stress triaxiality levels have been investigated by the FEM method and experimental observations in plane strain and plane stress cases respectively. It was found that the shape change of growing voids, the configurations of a blunting crack tip and the sizes of decreasing ligament between the void and the crack tip are strongly dependent upon the stress triaxiality levels. Under the condition of plane stress, the stress triaxiality on the ligaments of cracks are nearly the same for different specimen geometries, also the void growth, crack tip blunting asnd decreasing of ligament size are identical for various specimens with increasing load levels, which lead to the conclusion that the J_i-value is independent of specimen geometries. However, in the plain strain case, different void growth, crack tip blunting and decreasing in ligament size for various stress triaxiality levels directly caused the J_i-value to be dependent on the specimen geometries. It was found that when the void is linked to the blunting crack tip by the extrapolation to the zero ligament from FEM calculations, the J_i values, measured experimentally, are underestimated slightly.     

Determination of the fracture toughness of fabric reinforced composites by the J-integral approach

The fracture behaviour of a glass-fabric-reinforced epoxy composite has been investigated experimentally. Load-displacement curves for single-edge-notched specimens were obtained on an MTS system and the J-integral evaluated through its energy rate interpretation. J_c, the critical value of the J-integral, obtained directly for a₀/w > 0·4 and that obtained through an extrapolation procedure for a₀/w < 0·4 compare quite well. J_c appears to be independent of crack length for specimen widths between 15 and 45 mm. J_c for ±45° specimens is less than half that for 0/90 specimens.     

On the use of constraint parameter A2 determined from displacement in predicting fracture event

The constraint based fracture mechanics methodology, J–A₂ method, has been used to interpret cleavage fracture recently. In all previous studies, the constraint parameter A₂ was determined by stresses analytically calculated from finite element analyses (FEA). In the current paper, it is first demonstrated that A₂ can be measured during a fracture test using the crack tip opening displacement (CTOD). A single-edge-notched specimen under bending (SENB) is used to compare the A₂ values determined from δ₅ displacement and the stress components. Finally, cleavage fracture toughness values for A533-B reactor pressure vessel (RPV) steel at −40°C obtained from test programs at Oak Ridge National Laboratory (ORNL) and the University of Kansas (KU) are interpreted using the J–A₂ analytical model. Particular emphasis is placed on using the A₂ determined from CTOD to characterize the fracture event. It is demonstrated that the effects of crack depth (shallow vs deep) and specimen size (small vs large) on the fracture toughness from the test programs can be interpreted and predicted using J and the constraint level A₂ measured from the displacement.