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.     

The micropolar thermoelastic problem of uniform heat-flow interrupted by an insulated penny-shaped crack

The classical problem of uniform heat-flow disturbed by an insulated penny-shaped crack is solved in the context of micropolar elasticity. The mode II stress intensity factor, K_II is found to depend on two new non-dimensional parameters N and τ − N is a measure of the coupling of the displacement field with the microstructure or the medium (0 N √2) and τ is the ratio of a material characteristic length to the crack radius. K_II remains higher than its classical value when N > 0, τ > 0 and attains the classical value as N and τ vanish. A closed-form expression to K_II is obtained in the physically important limiting case of τ → 0 with N fixed. In this limit the relative increment in K_II, over its classical value, is found to be (1 − v')N² where v' is the micropolar Poisson's ratio.     

Growth mechanism of stress corrosion cracking in high strength steel

Stress corrosion crack growth rates are measured at sveral stress intensity levels for low-tempered 4340 steel in 0.1N H₂SO₄ solution. The characteristics of the growth rates are divided into three regions of stress intensity factors: Region I near K_1SCC; Region III near unstable fracture toughness, K_1SC; and Region II, which lies between the two. K_1SCC is the value of K at which no crack growth can be detected after 240 hr.

In order to explain these experimental results, the crack initiation analysis reported in a previous paper is extended to the growth rates. A detached crack initiates and grows at the tip of an already existing crack. When the detached crack reaches the tip of the main crack, the process repeats as a new existing crack.

A relationship between crack growth rate, v, and stress intensity factor, K, is obtained as a function of b/a and a = b + d, where b is the distance from the tip of the main crack to the detached crack, and d is the ydrogen atom saturated domain.

The experimental data are in good agreement with the theoretical values in Region II when a = 0.02 mm, b/a = 0.8, c₁/c₀ = 2.8 for 200°C tempered specimens and a = 0.015 mm, b/a = 0.7, c₁/c₀ = 3.0, ρ_b = 0.055 mm for 400°C tempered specimens, where ρ_b is a fictitious notch radius. The plateau part in Region II for 400°C tempered specimens is also successfully explained by the present theory. For Region III, the value of b/a will be almost equal to 1 because v → ∞ for b/a → 1. On the other hand, for Region I, b/a will be zero, since the value of v becomes negligibly small and no crack growth is observable.     

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.     

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.     

Shear lips on fatigue fractures in aluminium alloy sheet material

An analysis is made of shear lip width measurements and the transition of tensile mode fatigue cracks to shear mode fatigue cracks, as observed on fatigue crack surfaces of aluminium alloy sheet material. It could be shown that these phenomena were controlled by ΔK_eff, rather than K_max or ΔK. For crack growth in air the shear lip width was approximately proportional to (ΔK_eff)², but it was significantly larger than the estimated size of the reversed plastic zone. The initiation of shear lips, the transition from plane stress to plane strain along the crack front and the environmental effect on shear lips are briefly considered in the discussion.     

Fracture analysis of exfoliation in an aluminium alloy

A method of measuring stress corrosion crack growth rates in an aluminium alloy, using contoured double cantilever beam specimens, is described. Samples taken from these test pieces and examined under an optical microscope suggest that there are two distinct mechanisms of crack growth. At stress intensities below about 0.85K_IC, exfoliation corrosion occurs within the crack, producing a zone of damaged material of finite thickness, rather than a single crack. At very high values ofK_I, a process similar to “fast fracture” occurs.     

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.     

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.     

The growth of fatigue cracks through particulate sic reinforced aluminum alloys

Crack growth rates for large fatigue cracks in 12 variations of particulate silicon carbide reinforced aluminum alloy composites have been measured. Composites with seven different matrix alloys were tested, four of which were of precipitation hardening compositions, and those were tested in both as-extruded and peak aged conditions. Five of the materials were made by casting, ingot metallurgical methods and two of the alloys by mechanical alloying, powder metallurgical methods. For both manufacturing methods, primary fabrication was followed by hot extrusion. The fatigue crack growth curves exhibited an approximately linear, or Paris law, region, fitting the function da/dN = BΔK^s, and a threshold stress intensity factor, ΔK_th. As has been found for other materials, the coefficients B and s are correlated; for these composites In B= −16.4−2.1s. A correlation was also found between ΔK_th and s, and it was found possible to compute the magnitude of ΔK_th using a simple model for the threshold together with yield stress and SiC size and volume fraction. These results were explained using a relationship between ΔK_th and crack closure determined previously for unreinforced aluminum alloys. The path of fatigue crack growth is through the matrix for these composites, and SiC has the effect of altering the slip distance, therefore, the plasticity accompanying fatigue cracks. It was shown that all the crack growth rate curves were reduced to one equation having the form da/dN = B'ΔK_eff^s' where B' = 6.5 × 10^-9m/cy and s' = 1.7. A partly theoretical method for predicting fatigue crack growth rates for untested composites is given. Fatigue crack surface roughness was measured and found to be described by a fractal dimension, but no correlation could be obtained between surface roughness parameters and ΔK_th.     

Fatigue crack initiation and growth under mixed mode loading in aluminum alloys 2017-T3 and 7075-T6

Fatigue crack initiation and growth characteristics under mixed mode loading have been investigated on aluminum alloys 2017-T3 and 7075-T6, using a newly developed apparatus for mixed mode loading tests. In 2017-T3, the fatigue crack initiation and growth characteristics from a precrack under mixed mode loading are divided into three regions—shear mode growth, tensile mode growth and no growth—on the ΔK_I-ΔK_II plane. The shear mode growth is observed in the region expressed approximately by ΔK_II > 3MPa√m and ΔK_II/ΔK_I > 1.6. In 7075-T6, the condition of shear mode crack initiation is expressed by ΔK_II > 8 MPa√m and ΔK_II/ΔK_I > 1.6, and continuous crack growth in shear mode is observed only in the case of ΔK_I/ΔK_II, 0. The threshold condition of fatigue crack growth in tensile mode is described by the maximum tensile stress criterion, which is given by Δσ_θmax √2πr 1.6MPa√m, in both aluminum alloys. The direction of shear mode crack growth approaches the plane in which K_I decreases and K_II increases towards the maximum with crack growth. da/dN-ΔK_II relations of the curved cracks growing in shear mode under mixed mode loading agree well with the da/dN-ΔK_II relation of a straight crack under pure mode II loading.     

The solution of a displacement discontinuity for an anisotropic half-plane and its applications to fracture mechanics

By imaginal method the solution of displacement discontinuity for anisotropic half-plane is derived in this paper. According to the Betti's reciprocal theorem, the relationship between the stress intensity factor K_I and the increment Δv/Δa is established and numerical results of K_I are obtained by the twice calculation method. Furthermore, the problem of edge crack chopping is studied in great detail, and the area of contaction and stress intensity factor K_I are found. These results are very worthwhile for research of chopping fracture in theory.     

Effects of welding residual stresses on fatigue crack growth behaviour in butt welds of a pipeline steel

In the present test the fatigue crack growth rate in the parent plate, weld and cross-bond regions was measured and the results were correlated with the stress intensity range ΔK and the effective stress intensity range ΔK_eff. It is indicated that the welding residual stresses strongly affect the crack growth rate. For the weld metal and cross-bond compact tension specimens in which crack growth is along the weld line the fatigue crack growth rate increases as the crack grows. However, for the T compact tension specimen in which crack growth is perpendicular to the weld line at a constant value of applied ΔK the crack growth rate initially decreases as the crack grows. Particularly, at a low constant value of applied ΔK the crack growth rate obviously decreases and the crack fails to grow after short crack growth. When the crack grows to intersect the welded zone, the fatigue crack growth rate gradually increases as the crack grows further. It is clear that the effect of welding residual stresses on the crack growth rate is related to the position of the crack and its orientation with respect to the weld line. Finally, the models of welding residual stress redistribution in the compact tension specimens with the growing crack and its influence on the fatigue crack closure are discussed. It appears that for a butt-welded joint one of the crack closure mechanisms may be considered by the bend or rotation deformation of crack faces due to the welding residual stress redistribution as the fatigue crack grows in the welded joint.     

A general method for determining mixed-mode stress intensity factors from isochromatic fringe patterns

A general method is presented for determining mixed-mode stress intensity factors K_I and K_II from isochromatic fringes near the crack tip. The method accounts for the effects of the far-field, non-singular stress, σ_ox. A non-linear equation is developed which relates the stress field in terms of K_I, K_II, and σ_ox to the co-ordinates, r and θ, defining the location of a point on an isochromatic fringe of order N.

Four different approaches for the solution of the non-linear equation are given. These include: a selected line approach in which data analysis is limited to the line θ = π and the K---N relation can be linearized and simplified, the classical approach in which two data points at (r_m, θ_m) are selected where r_m/θ = 0; a deterministic method where three arbitrarily located data points are used; and an over-deterministic approach where m (>3) arbitrarily located points are selected from the fringe field.

Except for the selected line approach, the method of solution involves an iteractive numerical procedure based on the Newton-Raphson technique. For the over-deterministic approach, the method of least squares was employed to fit the K-N relation to the field data.

All four methods provide solutions to 0.1% providing that the input parameters r, θ, and N describing the isochromatic field are exact. Convergence of the iterative methods is rapid (3–5 iterations) and computer costs are nominal. When experimental errors in the measurements of r and θ are taken into consideration, the over-deterministic approach which utilizes the method of least squares has a significant advantage. The method is global in nature and the use of multiple-point data available from the full-field fringe patterns permits a significant improvement in accuracy of K_I, K_II, and σ_ox determinations.     

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.     

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.     

Fatigue crack-growth characteristics of two magnesium alloys

Magnesium alloys are being increasingly used for engineering applications. Fatigue crack-growth data have therefore been obtained for a high strength magnesium-Zr alloy and a medium strength, weldable magnesium-Mn alloy. The results of tests on sheet material are presented in terms of the range of stress intensity factor ΔK. Critical values of ΔK necessary for fatigue crack growth ΔK_c were also obtained. The behaviour of the two alloys was similar; both rates of crack growth and ΔK_c were sensitive to mean stress. Fatigue crack growth was entirely on a 90° plane with no sign of the transition to crack growth or 45° planes usually observed in sheet materials. This was ascribed to the effects of preferred orientation of the crystal structure.     

An evaluation of the chevron V-notched bend bar fracture toughness specimen

The chevron V-notched bend bar specimen recently proposed as a practical approach to the fracture toughness testing of brittle materials has been further evaluated. The accuracy of the stress intensity expression has been improved through experimental analysis. The applicability of this specimen for determining the environment induced cracking threshold, K_Iscc was also investigated. Fracture toughness results developed for Pyroceram 9606, 7079-T6 aluminum and the apparent K_Iscc value of AISI 4340 steel exposed to hydrogen sulfide gas show that the chevron V-notched bend bar specimen can yield data essentially identical to that developed with more conventional fatigue precracked specimens. However, results also show that when catastrophic failure of a specimen occurs rather than the expected stable crack growth, the test is invalid. Further work is required to resolve this complication.     

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.     

Relaxation of residual stress with fatigue loading

Investigations have been carried out to study the relaxation of the surface residual stress in 0.23% C steel due to the application of fatigue loading. The residual stress was induced in the specimen by pre-straining and was measured by X-ray back reflection method using Cr-K radiation. The surface residual stress induced, depends on the plastic strain and appears to bear a relation of the type σ_R = σ_o(e_p)^0.78. The decay of the residual stress appears to depend on log N, given by the relation σ_R1 = σ_RO−K log N, where N is the number of fatigue cycles. The constant K depends on the initial value of the residual stress.