Effects of temperature,initial stress intensity factor and loading speed on the crack branching in delayed failure

The relation between diffusion behavior of hydrogen atoms and crack branching in delayed failure was discussed.The hypotheses that diffusion paths of hydrogen atoms at crack tip broaden with increase of stress intensity factor $\text{K}$, and that crack branching occurs when hydrogen atoms diffuse through the position where stable cracks are to nucleate, can well explain the facts that crack branching occurs when $\text{K}$ reaches to a certain value, $\text{K}{}_{\mathrm{IB}}$, and that $\text{K}{}_{\mathrm{IB}}$ increases with increase of temperature. The initial stress intensity factor and loading speed do not actually influence $\text{K}{}_{\mathrm{IB}}$, which can also be explained by the above hypotheses.     

Mechanism of corrosion fatigue crack propagation in high strength steels

The crack propagation velocity in corrosion fatigue $\text{(d a/d N)}{}_{\mathrm{c}}$ were measured on the Ni-Cr-Mo steel quenched and tempered at 473 or 773 K.The steel with high sensitivity to delayed failure reveals the largest $\text{(d a/d N)}{}_{\mathrm{c}}$ under square load and the smaller $\text{(d a/d N)}{}_{\mathrm{c}}$ under positive saw tooth load. The frequency dependency of crack propagation characteristics indicates that the interaction between hydrogen atoms and the cyclic moving of triaxial position at crack tip acts an important role in the crack propagation mechanism, i.e. hydrogen concentration process controls the crack propagation of the steel.The steel with low susceptibility to delayed failure reveals, on the other hand, the largest $\text{(d a/d N)}{}_{\mathrm{c}}$ under the positive saw tooth load but the smallest $\text{(d a/d N)}{}_{\mathrm{c}}$ under the square load, i.e. the stress increasing time is important and the hydrogen invasion process is the controlling factor for the crack propagation.     

Influence of stress state on static crack growth in AlZnMgCuO·5

To investigate the influence of stress state on the $\text{R-}\text{curve}$ the electric potential method was used to determine $\text{R-}\text{curves}$ for specimens with different thicknesses. The maximum thickness was greater than 2.5 ($\text{K}{}_{\mathrm{Ic}}\text{/δ}{}_{\mathrm{Y}}$)². A formula developed by H.H. Johnson was used to compute the crack length increase from the measured potential drop.The investigation showed a marked influence of specimen thickness on the crack propagation resistance. This influence increases with increasing crack propagation. Transition from plane strain to plane stress causes an increase of the crack propagation resistance. The $\text{R-}\text{curve}$ is also dependent on specimen orientation with respect to rolling direction whereas a twofold variation of initial crack length did not show any influence on the $\text{R-}\text{curve}$. Furthermore, the experimental $\text{R-}\text{curve}$ data are compared with analytical $\text{R-}\text{curve}$ expressions.     

Crack tip closure and environmental crack propagation

Crack propagation rate, da/dN, and crack tip closure stress, σ_cc, in part-through crack fatigue specimens of aluminum alloys are drastically affected by gaseous environments. The present studies indicate that the crack closure reflects the influence of the environment on the plastic deformation at the crack tip, and, therefore, on the crack propagation rates. Postulating that da/dN is mainly determined by $\text{ΔK}{}_{\mathrm{eff}}\text{∝ (σ}{}_{\max }\text{?σ}{}_{\mathrm{cc}}\text{)}$ (instead of $\text{ΔK ∝ (σ}{}_{\max }\text{?σ}{}_{\min }\text{)}$, as is done traditionally) leads to the relationship $\text{da/dN = A(ΔK}{}_{\mathrm{eff}}\text{)}{}^{\mathrm{n}}$ in which $\text{A}$ and $\text{n}$ are virtually independent of the gaseous environment. The exponents are $\text{n ≈ 3.3}$ for Al 7075 T651 and $\text{n ≈ 3.1}$ for Al 2024 T351, respectively.     

Cyclic analysis of a propagating crack and its correlation with fatigue crack growth

Stress and strain field of a propagating fatigue crack and the resulting crack opening and closing behavior were analysed. It was found that a propagating fatigue crack was closed at tensile external loads due to the cyclically induced residual stresses. Strain range value $\text{Δ?}{}_{\mathrm{y}}$ in the vicinity of the crack tip was found to be closely related with the effective stress intensity factor range $\text{ΔK}{}_{\mathrm{eff}}$ which was determined on the basts of the analytical crack opening and closing behavior at its tip. Application of this analysis to the non-propagating fatigue crack problem and the fatigue crack propagation problems under variable stress amplitude conditions revealed that both $\text{Δ?}{}_{\mathrm{y}}$ and $\text{ΔK}{}_{\mathrm{eff}}$ were essential parameters governing fatigue crack growth rate.     

An experimental study of crack tip plastic flow in mild steel

The paper deals with an experimental study on the nature of plastic flow at the root of a crack in mild steel beams, for the non-valid $\text{K}{}_{\mathrm{IC}}$ test regime, under three point hending loads. Photoelastic coating technique has been used to measure the plasticity spread ahead of the tip in relation to the load-COD record. It is observed that in all cases there is a sudden increase in specimen compliance near the maximum linear load due to an abrupt increase in plastic zone size on some preferential planes ahead of the crack tip. This abrupt increase in plastic flow was seen to occur along the 45° planes (with respect to the plane of the crack) for thicker beams and/or with longer cracks. In contrast, the plastic zone extended more on the plane of the crack for thin section beams with relatively shorter cracks. The stress intensity factor required to cause this sudden loss of resistance to localized deformation is found to be remaining constant beyond a certain crack length for a given specimen thickness. These observations suggest that a critical stress intensity factor () concept can be introduced to describe the abrupt flow localization ahead of the crack tip. This () can be taken as a new parameter in addition to those commonly used in characterising the overall “fracture” behaviour of large scale yielding materials like mild steel, especially in the non-valid $\text{K}{}_{\mathrm{IC}}$ test regime.     

Dynamic stress distribution around the tip of a running crack

The stress distribution is obtained around the tip of a crack running in a brittle material. The stresses are written as the sum of the associated static solution and the wave-effect terms which depend upon the crack speed. The results obtained clearly reduce to the associated static solutions if the crack speed vanishes.Near the tip of the crack, the dynamic stress-intensity factor for the circumferential stress, $\text{σ}{}_{\mathrm{\theta \theta }}$, is written as the product of the associated static stress-intensity factor and the dynamic correction factor which is a nondimensional function of the crack speed, $\text{V}$, the angle from the crack plane, θ, and Poisson's ratio, ν. The value of the correction factor is computed for various values of $\text{V}$ and θ at $\text{ν = 0.25}$. It is shown that the maximum tensile value of $\text{σ}{}_{\mathrm{\theta \theta }}$, occurs on the crack plane for $\text{V}$ less than 0.7 time shear wave speed, $\text{c}{}_2$, and suddenly shifts to the plane of $\text{θ = 55°}$ for $\text{V}$ slightly larger than 0.7 $\text{c}{}_2$. For $\text{V > 0.7}$$\text{c}{}_2$, the angle θ for the maximum $\text{σ}{}_{\mathrm{\theta \theta }}$, θ being larger than 55°, varies continuously with the crack speed, $\text{V}$. The results obtained are used to discuss the growth of branching crack.     

On crack opening stress level in fatigue by Eddy current technique

Linear elastic fracture mechanics relates fatigue crack growth with the stress intensity factor at the crack tip. Presence of residual deformations at the tip of a fatigue crack reduces the crack tip stress intensification such that effective stress intensity range $\text{ΔK}{}_{\mathrm{e}}\text{= U · ΔK}$. In this paper use of eddy current technique is exhibited to find the values of test value of effective stress range factor $\text{U}{}_{\mathrm{test}}$. A reasonable comparison between computed and experimental results of $\text{U}{}_1$ and $\text{U}{}_{\mathrm{test}}$ on two Al alloys 6061-T6 and 6063-T6 has recommended the Eddy Current Technology for finding out the values of crack opening stress level under given loading conditions.     

A modified thickness criterion for fracture toughness testing

A modified criterion is developed on an empirical basis for the minimum thickness $\text{B}{}_{\min }$ of a plane strain fracture toughness test specimen: $\text{B}{}_{\mathrm{<mtext>min</mtext>}}\text{= 400}\text{K}{}_{\mathrm{Ic}}{}^2\text{Eδ}{}_{\mathrm{Y}}$ where $\text{K}{}_{\mathrm{Ic}}$ is the plane strain fracture toughness, $\text{E}$ is the Young's modulus and δ_Y is the yield stress of the material. The modified criterion is tested alongside the ASTM thickness criterion against published data on the variation of $\text{K}{}_{\mathrm{c}}$ with thickness, and shows significantly the better agreement with observed values of $\text{B}{}_{\mathrm{<mtext>min</mtext>}}$ for a wide range of materials.An attempt has been made to rationalise this criterion. The expression is considered to take into account two major factors which determine $\text{B}{}_{\mathrm{<mtext>min</mtext>}}$, the attainment of plane strain in the specimen interior ahead of the crack tip, and the role of microstructure in determining how far the quasi-plane strain fracture (square fracture) extends beyond the region of true plane strain.     

The condition of fatigue crack growth in mixed mode condition

The condition of the initiation of fatigue crack growth in mixed mode conditions has been investigated by using precracked low carbon steel specimens.It is pointed out that, firstly, the critical condition of crack growth should be defined with regard to the modes of fatigue crack growth, i.e. shear mode and tensile mode. Secondly, it is proposed that the critical condition of fatigue crack growth is given by the local tensile stress and shearing stress at the notch tip determined by stress intensity factors $\text{K}{}_{\mathrm{I}}$ and $\text{K}{}_{\mathrm{II}}$, and that this criterion is generally applicable to in-plane-loading conditions, i.e. Mode $\text{I}$, Mode $\text{II}$ and Mixed Mode conditions.     

Crack closure in 2219-T851 aluminum alloy

The effects of specimen thickness, stress ratio ($\text{R}$) and maximum stress intensity factor ($\text{K}{}_{\max }$) on crack closure (or opening) were studied using a 2219-T851 aluminum alloy. The crack length and the occurrence of crack closure were measured by an electrical potential method. The experimental work was carried out within the framework of linear-elastic fracture mechanics.The experimental results show that the onset of crack closure (or opening) dependes on $\text{R, K}{}_{\mathrm{<mtext>max</mtext>}}$), and specimen thickness. In terms of the “effective stress intensity range ratio” ($\text{U}$), as defined by Elber, the results show that $\text{U}$ tends to increase for increasing $\text{R}$, decrease for increasing $\text{K}{}_{\max }$, and decrease with increasing specimen thickness. From these trends, it is shown that the “effective stress intensity range” ($\text{ΔK}{}_{\mathrm{<mtext>eff</mtext>}}$) does not always increase with increasing stress intensity range ($\text{ΔK}$).The experimental results show that crack closure cannot fully account for the effects of stress ratio, specimen thickness and $\text{K}{}_{\max }$ on fatigue crack growth. The use of $\text{ΔK}{}_{\mathrm{<mtext>eff</mtext>}}$ as a parameter for characterizing the mechanical driving force for fatigue crack growth is questioned.     

Effect of stress wave shape on the crack propagation velocity in cyclic delayed failure

Crack propagation velocity in delayed failure under superposed repeating load, ($\text{d}\text{a/}\text{d}\text{t)}{}_{\mathrm{R}}$, was compared with that under static load, ($\text{d}\text{a/}\text{d}\text{t)}{}_{\mathrm{S}}$Two peaks appear on the relation between decreasing rate of crack propagation velocity, $\text{1-β = 1 ? (}\text{d}\text{a/}\text{d}\text{t))}{}_{\mathrm{R}}\text{/(}\text{d}\text{a/}\text{d}\text{t)}{}_{\mathrm{S}}$ and frequency, ?, both under sinusoidal and square load. By changing the ratio of holding time at maximum stress intensity factor to that at minimum stress intensity factor in square load, it was deduced that the existence of two peaks on the 1 ? β vs $\text{f}$ curve was caused by an asymmetric interaction between hydrogen atoms and cyclic moving of the position with triaxial tensile stress at crack tip. Moreover, the relation between 1 ? β and $\text{f}$ under the positive or negative saw tooth load could be well explained by the interaction model.     

A comparison of the geometry dependence of several nonlinear fracture toughness parameters

A number of fracture toughness tests on compact tension specimens have been performed for the purpose of comparing several nonlinear fracture toughness methods; including the nonlinear energy ($\text{G}\text{?}{}_{\mathrm{I}}$), J-integral ($\text{J}{}_{\mathrm{I}}$), COD ($\text{G}{}_{\mathrm{\delta }}$), and linear (–$\text{G}{}_{\mathrm{I}}$) approaches. The effect of variations in specimen thickness ($\text{B}$) and width ($\text{w}$) on the fracture toughness was examined for 7075-T651, 2124-T851, 2048-T35I, and 2048-T851 aluminum alloys, Ti-6Al-4V, and 4340 steel. Fracture toughness values were evaluated at both the initiation of stable crack growth and the onset of unstable fracture (peak load).It was found that the peak load toughness values are quite geometry sensitive at thicknesses below the requirement for plane strain fracture. At the initiation of stable crack growth, the toughness values are constant over a much larger range of specimen thickness. However, the nonlinearity of the load displacement curve is quite limited at this point and the associated fracture toughness is only 30–50% of the peak-load values.     

A method for determining the stress intensity threshold level for fatigue crack propagation

The influence of a decreasing rate of stress intensity factor with crack propagation, $\text{d}\text{K/}\text{d}\text{a}$, on a stress intensity threshold level, $\text{δK}{}_{\mathrm{th}}$, below which fatigue crack propagation becomes insignificant is investigated. Specimens, 200 mm wide, 10 mm thick with a 40 mm-long central crack, are fatigued at the decreasing rates, $\text{∥}\text{d(δK)}\text{d}\text{a∥}$, of 2,44, 5 and 10 kg/mm^5/2 with a peak load control system and a pair of crack followers. In this range of $\text{d}\text{(δK)/}\text{d}\text{a}$, the stress intensity threshold levels, $\text{δK}{}_{\mathrm{th}}$, have the same value regardless of $\text{d}\text{K/}\text{d}\text{a}$. Therefore, the present method of decreasing the stress intensity factor at a constant rate is suitable for determining the characteristic $\text{δK}{}_{\mathrm{th}}$ of materials. Furthermore, the influence of stress ratio, $\text{R}$, is investigated at the decreasing rate, $\text{∥}\text{d}\text{(δK)/}\text{d}\text{a]}$, of 10 kg/mm^5/2.     

Fatigue crack propagation in steels

From previous investigations of the mechanisms of both fracture and fatigue crack propagation, the static fracture model proposed by Lal and Weiss may be thought as reasonable for describing fatigue crack propagation in metals at both low and intermediate stress intensity factor ranges $\text{ΔK}$. Recent progress in fatigue crack propagation indicates that it is not only possible, but also necessary, to modify this static fracture model. Based on the modified static fracture model, the effective stress intensity factor range $\text{ΔK}{}_{\mathrm{eff}}$, which is defined as the difference between $\text{ΔK}$ and the fatigue crack propagation threshold value $\text{Δ}{}_{\mathrm{th}}$, is taken as the governing parameter for fatigue crack propagation. Utilising the estimates of the theoretical strengths of metals employed in industry, a new expression for fatigue crack propagation, which may be predicted from the tensile properties of the metals, has been derived. The correlation between the fatigue crack propagation rate and the tensile properties is thus revealed. The new expression fits the test results of fatigue crack propagation of steels below 10^?3 mm/cycle and indicates well the effect of stress ratio on the fatigue crack propagation rate.     

Fatigue crack propagation from a crack inclined to the cyclic tensile axis

Cyclic stresses with stress ratio R = 0.65 were applied to sheet specimens of aluminium which have an initial crack inclined to the tensile axis at angles of 30°, 45°, 72° or 90°. The threshold condition for the non-propagation of the initial crack was found to be given by a quadratic form of the ranges of the stress intensity factors of modes I and II. The direction of fatigue crack extension from the inclined crack was roughly perpendicular to the tensile axis at stress ranges just above the threshold value for non-propagation. On the other hand, at stress ranges 1.6 times higher than the threshold values the crack grew in the direction of the initial crack. The rate of crack growth in the initial crack direction was found to be expressed by the following function of stress intensity factor ranges of mode I, K₁, and mode II, K₂: $\text{dc}\text{dN}\text{= C(K}{}_{\mathrm{eff}}\text{)sum}$, where $\text{K}{}_{\mathrm{eff}}\text{= [K}{}_1{}^4\text{+ 8K}{}_2{}^4\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$. This law was derived on the basis of the fatigue crack propagation model proposed by Weertman.     

Experimental research on surface crack propagation laws for low alloy steel

Surface crack propagation experiments were performed for low alloy steel. The testing result shows that the data for the crack propagation rate in the surface in the direction of the width may be treated by using Paris and Erdogan formula [1] for the crack propagation rate, and Shah and Kobayashi's formula for the stress intensity factor[2]. For the crack propagation rate in the direction of the depth, the data obtained cannot be treated in this way.It has been found that the data can also be treated by using the experimental formula suggested by Kawahara et al.[3].In addition, a test for investigating through-thickness crack propagation was made. It was found that the propagation rate of the through-thickness crack is much greater than those of the surface crack both in the direction of the width and in the direction of the depth. When $\text{ΔK(= 100 Kg/mm}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$) is the same, the propagation rate of through-thickness crack da/dN is five times as great as that of surface crack in the direction of the width.During the propagation of the crack, the relationship between the crack length b and the crack depth a is $\text{a}\text{b}\text{= A?B}\text{a}\text{h}$, where A = 0.97, B = 1.29.With db/dN determined, the prediction of fatigue life can be calculated by

$\text{N=}\text{∫}\text{a}{}_0\text{a}\text{A}\text{A?B}\text{a}\text{h}{}^2\text{d}\text{N}\text{d}\text{b}\text{d}\text{a}$

.     

A correlation between dynamic initiation toughness and crack arrest toughness

Dynamic initiation toughness values were obtained from testing small 3-point bend specimens at ?50, ?25, 0, +23°C. Two specimen orientations were tested which showed no marked difference in critical dynamic initiation toughness. The obtained $\text{K}{}_{\mathrm{Id}}$ data were correlated with the crack arrest toughness $\text{K}{}_{\mathrm{Im}}$ and $\text{K}{}_{\mathrm{Ia}}$. The value of $\text{K}{}_{\mathrm{Id}}$ is in the range 0.93 to 1.29 times the corresponding fast fracture toughness, $\text{k}{}_{\mathrm{im}}$ while the ratio $\text{K}{}_{\mathrm{Id}}\text{/K}{}_{\mathrm{Ia}}$ varies between 1.27 and 1.60.     

The stress field near the blunt crack tip and the fracture criterion

The asymptotic expansion solution containing two terms for the stress field near the blunt crack tip is obtained. It is proposed that the slit be divided into the ideal crack, blunt crack I, blunt crack II and the notch in accordance with the geometrical structure of the slit tip. Whether the blunt crack can be considered as the ideal crack will depend mainly on the following three factors: $\text{√}\text{2R}{}_0\text{C}$, $\text{√}\text{R}{}_0\text{r}{}_{\mathrm{c}}$ and the profile of the crack. In this paper, the influence of the crack tip radius on the fracture criterion is studied and it is shown that the classical strength theories belong to the unconditional extremum criteria while the S criterion, etc. in fracture mechanics belong to the conditional extremum criteria. A modified maximum tension stress theory is developed, in which the fracture theories of the crack and the notch can be roughly unified.     

Vertical crack inside a semi-infinite plane

In this paper we consider the problem of determining the stress-intensity factors and the crack energy in a semi-infinite plane containing an inside crack perpendicular to the straight boundary of the plane. By the use of Mellin transform, we reduce the problem to solving a single singular integral equation. Approximate solution of the integral equation is obtained as a series of Chebyshev polynomials of the first kind. The coefficients $\text{B}{}_{\mathrm{n}}$ of the series are determined from a system of linear algebraic equations. Expressions for the stress-intensity factors at the edges of the crack, the shape of the crack and the crack energy are derived in terms of the coefficients $\text{B}{}_{\mathrm{n}}$. The numerical values of these quantities have been displayed graphically for three particular cases.