Fracture behaviour of dynamically loaded ship building plate material

The fracture toughness values of ship building mild steel measured over a temperature range ? 196°C to 28°C and crack tip strain rates ranging from 10^?5/sec to 10^?1/sec are examined in the light of the models recently proposed by Malkin and Tetelman. The effect of a change in inclusion morphology brought about by electroslag refining on the fracture toughness of the steel is also evaluated. It is found that the stress-induced fracture criterion ofthe model applies for the case where the ratio $\text{σ}{}^1{}_{\mathrm{f}}\text{σ}{}_{\mathrm{YS}}\text{? 3.94}$. This ratio is independent of the strain rate. In the strain induced fracture region of the model, the critical strain near the crack tip, ?_f(Rβ) is a function of the yield stress irrespective of temperature and strain rate. Electroslag refining reduces significantly the size and volume fraction of the inclusions and changes their shape from prolate ellipsoid to spherical. Apparently the electroslag refining does not improve fracture toughness significantly if the fracture toughness of the as received material measured with the major axis of the inclusions perpendicular to the crack front, is taken as a basis of comparison.     

Fatigue crack propagation work coefficient—a material constant giving degree of resistance to fatigue crack growth

Study on fatigue crack growth in steels was carried out from energetic point of view, i.e. taking account of plastic work around the fatigue crack. Based on the examination of the relation between fatigue crack growth rate (da/dN) and the plastic work around the fatigue crack tip (W_0.02 in SUS304, Fe-3Si and HT 60 steels, a material constant-fatigue crack propagation work coefficient-Q_0.02 is proposed. It is the ratio of W_0.02 to da/dN and means the degree of the resistance to fatigue crack growth. Numerical expression of Q_0.02 by mechanical properties was derived, which is given by

$\text{Q}{}_{0.02}\text{=}\text{9.3x10}{}^1\text{(σ}{}_{\mathrm{y}}\text{+σ}{}_{0.2}\text{)}\text{σ}{}_{\mathrm{y}}{}^{1.3}$

Comparison of Q_0.02 of various steels showed that Q_0.02 of high strength steels is very small compared with that of low strength steels. Graphical representation of the relation between Q_0.02 and da/dN at various values of ΔK/σ_y for steels revealed that da/dN at given value of ΔK/σ_y increase with decreasing Q_0.02. It is shown that fatigue crack growth behaviour of a steel (da/dN-ΔK relation) can be obtained from the Q_0.02-da/dN diagram by knowing the mechanical properties. Discussion on design stress level of the steels is also given.     

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.     

Studies on crack growth rate under high temperature creep,fatigue and creep-fatigue interaction—II: On the role of fracture mechanics parameter aeffσg

For high temperature creep, fatigue and creep-fatigue interaction, several authors have recently attempted to express crack growth rate in terms of stress intensity factor $\text{K}{}_{\mathrm{I}}\text{= α}\text{aσ}{}_{\mathrm{g}}$, where a is the equivalent crack length as the sum of the initial notch length a₀ and the actual crack length $\text{a}{}^1$, that is, $\text{a = a}{}_0\text{+ a}{}^1$. On the other hand, it has been shown by Yokobori and Konosu that under the large scale yielding condition, the local stress distribution near the notch tip is given by the fracture mechanics parameter of $\text{aσ}{}_{\mathrm{g}}\text{?(σ}{}_{\mathrm{g}}$), where a is the cycloidal notch length, σ_g is the gross section stress and $\text{?(σ}{}_{\mathrm{g}}$) is a function of σ_g. Furthermore, when the crack growth from the initial notch is concerned, it is more reasonable to use the effective crack length a_eff taking into account of the effect of the initial notch instead of the equivalent crack length a. Thus we believe mathematical formula for the crack growth rate under high temperature creep, fatigue and creep-fatigue interaction conditions may be expressed at least in principle as function of $\text{a}{}_{\mathrm{eff}}\text{σ}{}_{\mathrm{g}}\text{, σ}{}_{\mathrm{g}}$ and temperature.In the present paper, the geometrical change of notch shape from the instant of load application was continuously observed during the tests without interruption under high temperature creep, fatigue and creep-fatigue interaction conditions. Also, the effective crack length a_eff was calculated by the finite element method for the accurate estimation of local stress distribution near the tip of the crack initiated from the initial notch root. Furthermore, experimental data on crack growth rates previously obtained are analysed in terms of the parameter of $\text{a}{}_{\mathrm{eff}}\text{σ}{}_{\mathrm{g}}$ with gross section stresses and temperatures as parameters, respectively.     

Fracture of thin sections containing surface cracks

Surface-cracked specimens of several thicknesses of 7075-T651 and 7075-T6 aluminum were tested in uniaxial tension. For thicknesses t less than 0.25 in., the gross fracture stress σ_f of 7075-T651 Al was empirically related to flaw size by the following expression:

$\text{δ}{}_{\mathrm{f}}\text{σ}{}_{\mathrm{ult}}\text{= 1 + S(}\text{a}\text{φ}{}^2\text{.t}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$

where σ_ult is the ultimate strength, a the crack depth, φ a function of crack shape, and S a proportionality constant equal to ?1.7 in.^{$\text{?1}\text{2}$}. For 0.25-in. thick 7075-T651 aluminum, σ_f was found to obey this relationship only when $\text{a}\text{φ}{}^2$ is less than 0.065 in.; for larger flaws, such that $\text{0.065 <}\text{a}\text{φ}{}^2\text{< 0.11, σ}{}_{\mathrm{f}}$ is better predicted by Irwin's surface-crack equation with an apparent K_IC value of $\text{32.2}\text{ksi-in.}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$.Fracture data for thin sections of 2014-T6 and 2014-T651 Al tested at ?423°F are analyzed in terms of the empirical relationship above and are found to be in good agreement. For these alloys, S has a value of ?2.6 in.^{$\text{?1}\text{2}$}.Applicability of the empirical relationship and Irwin's surface-crack analysis to the fracture of thin sections is discussed in terms of crack size, section thickness, and plastic zone size.     

Kinetics of subcritical cracking under the chloride and sulphide environments in a low alloy steel

The effects of two aqueous environments, namely chloride and sulphide have been investigated using fracture mechanics approaches in a Ni-Cr-Mo alloy, tempered between 200–600°C temperatures after quenching. The experimental investigation included tensile and fracture toughness tests in the ambient condition, environmental tests to determine the threshold, K_ISCC and the crack growth rate values $\text{da}\text{dt}$ and fracture surface studies. An attempt has been made to substantiate the role of microstructure and the source of hydrogen on the susceptibility to failure by computing $\text{C}{}_{\mathrm{c}}\text{C}{}_{\mathrm{o}}$ ratios for the hydrogen induced cracking process. A crack growth rate expression of the type, $\text{da}\text{dt}\text{= c'(K)}{}^{\mathrm{n}}$ is proposed for Stages I and II to account for the discrepancy between the theoretically calculated and the experimental $\text{da}\text{dt}$ data. The experimental values of the constants c' and n are determined. For all the tempering conditions investigated, the H₂S environment appears to be more hostile than the NaCl medium. However, the susceptibility to both the environments is more pronounced for yield strength values greater than 1500 MPa. The $\text{K}{}_{\mathrm{If}}\text{K}{}_{\mathrm{IC}}$ ratio is bound to be less than 1 under the H₂S, and greater than 1 under the NaCl solution.     

Fracture initiation under impact

In the first part of this paper the influence of temperature T and loading rate K_I upon the fracture toughness K_IC of structural steels is considered. A review of experimental results is presented over a wide range of loading rate and temperature in the form of the cross-sections of the constitutive surface K_INC = f(K_I,T). The hypothesis is proposed that both yield stress σ_y in uniaxial tension and fracture toughness K_IC are controlled by the same process of thermally activated movements of dislocations. Consequently, an introduction of the characteristic time t_c leads to the master plot K_IC (σ_y) in double logarithmic coordinates which is temperature and rate-independent. Such an approach provides a simple method for estimating the value of K_IC under a given set of imposed conditions (T,K?_I)₁ provided it is known for another set of imposed conditions (T,K?_I)₂.In the next part of this paper an attempt is presented to model the effect of T and K?_I on fracture toughness K_IC [15]. A model is discussed which combines correlations between critical cleavage stress σ_F, yield stress σ_y and the concept of thermally activated plastic flow from side and the local fracture criteria from the other [15]. It has been demonstrated that this approach can be useful in the proper predictions of changes of K_IC as a function of loading rate and temperature. For some steels, however, a minimum of fracture toughness is observed and typically occurs for $\text{K}{}_{\mathrm{I}}\text{? 1×10}{}^4$ MPa/pv/m/s at room temperature. The last part of this study deals with this important phenomenon [34]. It is concluded that the behavior of the constitutive surface K_IC = f(K_I,T) is highly nonlinear for steels.     

An examination of mixed fatigue-tensile surface crack growth in rails

The fracture instability associated with alternating periods of fatigue and tensile growth of surface cracks was investigated in steel rails. Three different steels were tested. The instabilities commenced when the maximum stress intensity factor $\text{K}$ exceeded the fracture toughness $\text{K}{}_{\mathrm{IC}}$ and resulted in crack jump or total rail failure. The conditions for the establishment of fatigue-tensile crack jump and arrest are described. The load level, residual stresses, crack geometry and fracture toughness effects are analysed. The fatigue surface cracks were penetrated in both stress relieved and stress unrelieved rails. The effective stress intensity factors including the contribution of the applied load and residual stresses were calculated. For both the fatigue-tensile and tensile-fatigue transitions the stress intensity factors were almost the same with the value for the tensile-fatigue transition being slightly lower. Both calculated stress intensity factors were close to the fracture toughness $\text{K}{}_{\mathrm{IC}}$.     

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.     

A model for fatigue crack growth in a threshold region

The prediction of fatigue crack growth at very low ΔK values, and in particular for the threshold region, is important in design and in many engineering applications. A simple model for cyclic crack propagation in ductile materials is discussed and the expression

$\text{da}\text{dN}\text{=}\text{2}{}^{\mathrm{1+n}}\text{(1?2v)(ΔK}{}^2{}_{\mathrm{eff}}\text{?ΔK}{}^2{}_{\mathrm{c,eff}}\text{)}\text{4(1+n)π σ}{}^{\mathrm{1?n}}{}_{\mathrm{yc}}\text{E}{}^{\mathrm{1+n}}\text{?}{}^{\mathrm{1+n}}{}_{\mathrm{f}}$

developed. Here, n is the cyclic strain hardening exponent, σ_yc is cyclic yield, and ε_f is the true fracture strain. The model is successfully used in the analysis of fatigue data BS 4360-50D steel.     

Strain rate effects on viscoelastic crack bifurcation

The effects of applied strain rate on the viscoelastic crack bifurcation phenomenon in Polymethyl Methacrylate (PMMA) were investigated. It was still verified that the product $\text{σ}{}_{\mathrm{f}}\text{C}{}_{\mathrm{b}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ was constant, as was already observed by Congleton and Petch, and Anthony, Chubb and Congleton, for brittle elastic materials, for any strain rate, where σ_f = the gross fracture stress and C_b= the main crack length until the bifurcation starts. However, it was found that the higher strain rate increases the main crack length C_b resulting in the decrease in the gross fracture stress σ_f and vice versa. This might be interpreted that the higher stress concentration at the initiation crack tip, which is realized by becoming more brittle due to the higher strain rate owing to the predominance of the elastic element in the viscoelastic material, decreases the gross fracture stress leading to the longer main crack length.     

Prior-to-failure extension of flaws under monotonic and pulsating loadings

An equation governing the prior to failure crack propagation is proposed. For a rate-sensitive solid containing two-dimensional crack and subject to the tensile mode of fracture the differential equations are integrated numerically for the loads increasing monotonically in time. The resulting integral curves gs = σ(l) and l= l(t), i.e. load vs crack length and length vs time, indicate that the growth of cracks in the subcritical range is strongly rate dependent.The fatigue growth, viewed as a sequence of slow growth periods, is simulated on EAI 380 analogue computer. The fourth power law proposed by Paris is confirmed only within certain range of high-cycle fatigue propagation and for a rate-insensitive solid. Otherwise, that is for a more pronounced rate dependency induced by viscosity of a solid and/or in the proximity of the final instability point the growth is markedly enhanced. For sufficiently small ratios of the applied stress intensity range ΔK to the toughness K_c, the suggested fatigue growth law consists of two terms, i.e.

$\text{d}\text{l}\text{d}\text{n}\text{=}\text{l}{}_1\text{12}\text{4}\text{ΔK}\text{K}{}_{\mathrm{c}}{}^4\text{+Cf}{}^{\mathrm{?1}}\text{ΔK}\text{K}{}_{\mathrm{c}}{}^2\text{, l}{}_1\text{=}\text{πK}{}^2{}_{\mathrm{c}}\text{8Y}{}^2$

First term is the familiar Paris expression while the second one accounts for the rate-dependent contribution; f denotes frequency and Y is the yield strength. Rate-sensitivity C is defined by eq. (1.13).     

G̃c and R-curve fracture toughness values for aluminum alloys under plane stress conditions

The effect of specimen geometry and subcritical crack growth on the nonlinear energy fracture toughness, $\text{G}\text{?}{}_{\mathrm{c}}$, has been examined for thin, center-cracked sheets of 2024-T3 and 7075-T6 aluminum alloys. The procedure followed was to independently vary the specimen length, L, width, w, andd crack length-to-specimen width ratio and to determine the toughness both at the onset of subcritical crack growth and at the initiation of unstable fracture. Comparisons were also made with the R-curve toughness, G_R, evaluated at unstable fracture from which it was found that both $\text{G}\text{?}{}_{\mathrm{c}}$ and G_R displayed the same trend of change with geometrical variables, with $\text{G}\text{?}{}_{\mathrm{c}}$ consistently higher than G_R. When the nonlinear energy fracture toughness was evaluated at the onset of subcritical crack growth, it was found that the geometry dependence essentially disappeared.Scanning electron microscopic examination of some typical fracture surfaces showed that stable crack growth was accompanied by a gradual change of fracture mode from plane strain to plane stress. An analysis of possible errors in the experimental procedure showed that the scatter observed in $\text{G}\text{?}{}_{\mathrm{c}}$ values was not due to experimental errors, but apparently due to inhomogeneities in the materials. Several techniques were also introduced for the purpose of more directly incorporating crack growth into the $\text{G}\text{?}{}_{\mathrm{c}}$ determination, but it was found that they did not cause significant variation in the toughness values.     

Effect of mechanical properties of material on rate of fatigue crack propagation

Many experimental and analytical equations on a rate of a fatigue crack propagation have been proposed. However, it seems that they can not fully express its complex behavior. There are still many problems remaining to be solved in order to clarify its mechanism. One of them is to clarify the relation between the rate of the crack propagation and the mechanical properties of material. In this paper, the rate of the crack propagation is analysed to clarify this problem. This analysis is based on the observation results of the fatigue crack propagation behavior previously by the authors. The analytical result is compared with the experimental one to make sure that they agree with each other. The conclusion obtained is; the rate of fatigue crack propagation is expressed by using the stress intensity factors as

$\text{dl}\text{dN}\text{= {}\text{c}\text{[Y}{}^2\text{F}{}^{\mathrm{a}}\text{E}{}^{\mathrm{a(1?n)}}\text{]}\text{} (K}{}_{\max }\text{)}{}^2\text{(K}{}_{\mathrm{a}}\text{)}{}^{\mathrm{a(2?n)}}$

. where C is a constant; E, Young's modulus; F, plastic coefficient; Y, yield stress; K_max and K_a, maximum and amplitude of the stress intensity factor, and α and n, exponents of the Manson-Coffin's law and work-hardening.     

Fracture toughness of H-11 steel and its susceptibility to stress corrosion cracking

The plane strain fracture toughness, $\text{K}{}_{\mathrm{IC}}$, was measured for H-11 steel using compact tension specimens after two separate heat treatments; one to provide good mechanical properties for normal engineering applications. Rc 46, 195 ksi yield strength, and the ofter heat treatment to provide maximum strength, Rc 56, 245 ksi yield strength. The Rc 46 samples exhibited no subcritical crack growth in either steam distilled water or hydraulic oil at $\text{K}{}_{\mathrm{I}}$ levels approaching 95% of the specimens' $\text{K}{}_{\mathrm{IC}}$ with times exceeding 20 hr. The Rc 56 samples under constant displacement loading exhibited subcritical crack growth in steam distilled water with a measured $\text{K}{}_{\mathrm{Iacc}}$ of 17.8 ksi √(in). The specimens were subjected to the environment just prior to loading, subcritical crack growth commenced without an incubation period, and both the $\text{K}{}_{\mathrm{I}}$ and crack growth increased with time. No subcritical crack growth was encountered in hydraulic oil at $\text{K}{}_{\mathrm{I}}$ levels approaching 98% of the specimens' $\text{K}{}_{\mathrm{IC}}$ with times exceeding 24 hr.     

The plastic zone and growth of fatigue cracks in magnesium MA12 alloy at room and low temperatures

The plastic zone formed at the fatigue crack tip and the fracture topography in MA12 magnesium alloy samples, tested at 293 and 140 K in air and in vacuum, were analysed. It was found that the plastic zone formed in vacuum is characterized by a greater size ($\text{h}$) and degree of plastic strain that in air, and the crack growth rate ($\text{d}\text{l/}\text{d}\text{N}$) is lower. Temperature reduction leads to a decrease in $\text{h}$, while $\text{d}\text{l/}\text{d}\text{N}$ and the fracture mechanism are affected by temperature ambiguously, depending on the alloy microstructure and the $\text{K}{}_{\mathrm{<mtext>max</mtext>}}$ value. It was established that the size of the plastic zone can be described by the equation:

$\text{h=A}\text{(}\text{K}{}_{\max }\text{σ}{}_{\mathrm{0.2ps}}\text{)}{}^2$

where $\text{A}$ is a coefficient dependent on the alloy structural state, environment and test temperature. Evaluation of the cyclic plastic zone size at $\text{K}{}_{\mathrm{<mtext>max</mtext>}}$, corresponding to the transition from a low temperature region to a ‘Paris’ region, showed that this transition occurred when the cyclic plastic zon reached the structural parameter of the material.     

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.     

Precracking high speed steel for fracture toughness testing

Fracture toughness testing of high speed steel, which has a high fatigue strength and low fracture toughness, is a problem because fatigue cracks are difficult, or impossible, to initiate at a maximum fatigue stress intensity of $\text{0.7 K}{}_{\mathrm{<mtext>IC</mtext>}}$, as specified. A method of initiation by the use of an electric pen and subsequent fast propagation by fatigue has been studied and a procedure developed to give accurate, reproducible values of $\text{K}{}_{\mathrm{<mtext>IC</mtext>}}$ on subsequent fracture toughness testing.     

Effect of loading history on stress corrosion cracking in high strength steel

The effect of preloading on crack nucleation time was examined with compact tension specimens having various notch radius in 0.1N-H²SO⁴ aqueous solution for 200°C tempered AISI 4340 steel. Crack nucleation time t_n increases by preloading for a given apparent stress intensity factor K_p2. The curve K_?2 vs. t_n deviates upward from the curve for the non preloading case. A linear relationship between the crack nucleation time and parameter is seen in semi-log diagram, where is taken as the value at t_n=α due to preloading. The apparent threshold stress intensity factor increases with K_?2 which is the apparent stress intensity factor of preloading. A detached crack is nucleated at some distance from the notch root and extends in a form of circle. This distance increases with increasing K_?2. The effect of load reduction during crack growth was examined. When the K-value was reduced from K₁ to K₂, an incubation time was observed before the crack started growing under the K₂-value. The incubation time t_m tends to increase with increasing ΔK = K₁-K₂. The threshold stress intensity factor was also found to increase for high load reduction.In order to explain these experimental results, a new dislocation model is proposed on the basis of stress induced diffusion of hydrogen in high stress region ahead of the notch root or a crack. This model suggests that the change in the crack nucleation time and the increase of the incubation time due to preloading or load reduction are caused by reducing the hydrostatic pressure and by spreading the hydrogen saturated region which requires more time for the hydrogen accumulation due to preloading or load reduction. The theory predicts the experimentally observed relations between and t_n and between log t_in and ΔK.     

A synergistic fracture mechanics approach to fatigue life evaluation

A technique for modeling synergistic effects in fatigue crack propagation (FCP) is presented. First, a mission (load/temperature history) is segregated into elemental damage events. A simple three parameter model is then used to describe these events. The model coefficients are seen to be interrelated linear functions of FCP rate controlling variables such as frequency, temperature, stress ratio (σ_min/σ_max), dwell, overload ratio ($\text{P}{}_{\mathrm{overload}}$/$\text{P}{}_{\max }$) and cycles between overload. Finally, integrating event-by-event crack advance gives the expected component crack propagation life under mission cycling. Results of this procedure applied to gas turbine disk materials IN100 and Waspaloy are discussed to examine the accuracy of the model.