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.     

A study of the size-effect on plastic energy dissipation and toughness in 2024-T3 aluminum alloy sheets

The plastic energy dissipation before crack growth initiation and during stable crack growth was determined in centercracked thin sheet specimens of 2024-T3 aluminum alloy with different width and crack length-to-width ratios. The plastic energy dissipation rate versus stable crack growth curve was found to be approximately linear, but the slope decreased considerably with increase in crack length. No correlation was observed between plastic energy dissipation rate and the linear toughness ($\text{G}\text{?}{}_{\mathrm{c}}$), the nonlinear energy toughness ($\text{G}\text{?}{}_{\mathrm{c}}$) or the $\text{R-}\text{curve}$ toughness ($\text{G}{}_{\mathrm{R}}$). The role of net section yielding on the decrease in stable crack growth and toughness values in small specimens is discussed.     

Determination of nonlinear energy toughness values for cyclic loading applications

For several years the nonlinear energy method proposed by Liebowitz and Eftis has been examined as a failure criterion for static testing of center-cracked and compact tension specimens. Since the method appears to be valid under conditions of crack-tip plasticity, subcritical crack growth and load relaxation, tests have been conducted to ascertain the merit of this method as a failure criterion under cyclic loading conditions. The nonlinear energy toughness for cyclic loading, $\text{G}\text{?}{}_{\mathrm{fc}}$, is obtained from an envelope of the cyclic load-displacement record, which naturally imposes some restrictions on the loading program.The cyclic toughness parameter, $\text{G}\text{?}{}_{\mathrm{fc}}$, has been evaluated for thin, center-cracked sheets of 2024-T3 and 7075-T6 aluminum alloys. The specimen dimensions were held constant and the load parameters were varied so that a significant variation of the cyclic life was obtained. Both alloys exhibited a significant reduction of $\text{G}\text{?}{}_{\mathrm{fc}}$ with increasing cyclic life in a manner similar to the classical $\text{S-N}$ diagram. For example, the ratio of cyclic to static toughness, $\text{G}\text{?}{}_{\mathrm{fc}}\text{/G}{}_{\mathrm{c}}$, was found to be about 0.8 when failure occurred after approximately 150 cycles. There appeared to be a tendency for the curve to level off at this point, which suggests that these curves may represent compressed S-N curves. It is felt that this method may serve the design process by allowing the establishment of a fracture toughness parameter capable of including the effects of the entire loading history of a structure into the fracture toughness requirements.     

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.     

Crack initiation from a sharp notch and stretched zone

The “crack tip COD” at the fracture initiation mainly consists of the stretched zone, the new surface which appeared due to the slip deformation at the notch tip. Therefore, the COD or the stretched zone width at the fracture initiation is a very important parameter which reflects the notch tip behavior until fracture initiation.In the case of fibrous crack initiation, the stretched zone width ($\text{S}{}_{\mathrm{i}}$) and COD ($\text{δ}{}_{\mathrm{i}}$), where $\text{δ}{}_{\mathrm{i}}$ ≈ √2 $\text{S}{}_{\mathrm{i}}$, take almost constant values regardless of temperature, specimen geometry, preloading (if the total $\text{δ}{}_{\mathrm{i}}$ is taken), slit angle (in the case of mixed mode condition) and so on, while, in the case of cleavage fracture initiation, COD and the stretched zone width take various values between the value at the fibrous crack initiation ($\text{δ}{}_{\mathrm{i}}$ or $\text{S}{}_{\mathrm{i}}$) and almost zero, depending on temperature and plastic constraint.     

The use of small specimen strength ratio for measuring fracture toughness

The specimen strength ratio ($\text{R}{}_{\mathrm{s}}$), determined from small specimen tests was correlated with plane strain fracture toughness ($\text{K}{}_{\mathrm{Ic}}$) values for many heats of A533B-1 steel. A variety of loading rate and specimen size results suggest that $\text{K}{}_{\mathrm{Ic}}$ can be predicted from the small specimen strength ratio up to values of $\text{R}{}_{\mathrm{s}}$ near 2.0. Also, conservative estimates of cleavage-initiated, elastic-plastic fracture toughness can extend beyond $\text{R}{}_{\mathrm{s}}$ values of 2.0. The ASTM E399 size criterion appears to be too restrictive for the class of steel studied, and a more appropriate requirement would reduce the ASTM criterion by a factor of four.     

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.     

On fracture toughness in the nonlinear range

A general definition of fracture toughness, designated by $\text{G}\text{?}{}_{\mathrm{c}}$, is developed which is appropriate to situations of subcritical crack growth and/or large-scale crack border plastic yield. The theoretical basis as well as comparisons with other proposed measures of fracture toughness are also discussed. A simple method is given for evaluating $\text{G}\text{?}{}_{\mathrm{c}}$ which is based on use of the load-displacement test record.     

Fracture toughness characterization of several aluminum alloys in semi-brittle fracture

A method has recently been developed for determining a nonlinear fracture toughness parameter defined by the relation $\text{G}\text{?}{}_{\mathrm{c}}\text{=}\text{C}\text{?}\text{G}{}_{\mathrm{c}}$ where G_c is the critical elastic strain energy rate as defined by Irwin. The $\text{C}\text{?}$ term is a function of the nonlinearity of the load-displacement test record and has been evaluated using the three parameter Ramberg-Osgood approach, although other curve fitting techniques could be applied as well. The method is quite straightforward and is applicable to plane stress, plane strain and mixed mode testing although only plane stress conditions are considered in this paper. For the case of a linear load-displacement record $\text{C}\text{?}\text{→ 1}$ and $\text{G}\text{?}{}_{\mathrm{c}}$ reduces to the linear elastic result.The toughness parameter $\text{G}\text{?}{}_{\mathrm{c}}$ has been evaluated for a number of high strength aluminum alloys and compared with published G_c values for these materials. The tests were conducted on center-cracked sheets of 2014-T6, 2024-T81, 7075-T6 and 7475-T61 aluminum alloys under conditions of varying specimen geometry and displacement gage length. It was found that the values of $\text{G}\text{?}{}_{\mathrm{c}}$ obtained from displacement readings with a gage length of 2 in. generally agreed with published values of $\text{G}{}_{\mathrm{c}}\text{=}\text{K}{}_{\mathrm{c}}{}^2\text{E}$. The $\text{G}\text{?}{}_{\mathrm{c}}$ values were found to vary inversely with gage length and a/w ratios. The variation in values for $\text{G}\text{?}{}_{\mathrm{c}}$ is of the same order of magnitude as the scatter in published values for G_c. However, $\text{G}\text{?}{}_{\mathrm{c}}$ appears to be less sensitive than G_c to changes in a/w.     

The effects of load ratio on environmentally assisted fatigue crack growth

A modification to the model of Weir et al. for surface reaction and transport controlled fatigue crack growth has been developed to explicitly account for the effect of load ratio on environmentally assisted fatigue crack growth. Load ratio was found to affect principally gas transport to the crack tip, and therefore affected only transport controlled crack growth response. Experimental verification of the modified model was made by studying the room temperature fatigue crack growth responses at different load ratios for a 2219-T851 aluminum alloy exposed to water vapor.The results show that the effects of load ratio can be attributed to two different sources—one relating to its effect on local deformation at the crack tip and is reflected through the mechanical component, (d$\text{a}$/d$\text{N}$)₀ and the other on its role in modifying environmental effect and is manifested through the corrosion fatigue component, $\text{(da/dN)}{}_{\mathrm{cf}}$ Furthermore, the results show that the saturation value of corrosion fatigue component, $\text{(da/dN)}{}_{\mathrm{cf,s}}$, is essentially independent of $\text{R}$, and that the exposure needed to produce “saturation response” ($\text{P}{}_0\text{/2f)}{}_{\mathrm{s}}$, as a function of load ratio can be predicted from the modified model. The modified model, therefore, allows one to predict the corrosion fatigue crack growth response for any load ratio on the basis of measurements made at a single load ratio, provided that the values of ($\text{da/dN}$), are known.     

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 $\text{K}{}_{\mathrm{IC}}$.     

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.     

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.     

The J-integral fracture criterion under opening and tearing modes and unloading effects

Measurements of $\text{J}$ from certain formulae agree well with compliance measurements for a round notched bar specimen subjected to tensile (Mode I) and torsional (Mode III) loadings. Crack growth resistance curves ($\text{R-}\text{curves}$) obtained by a three parameter technique are compared with those obtained by two current approaches. The $\text{J}{}_{\mathrm{IC}}$ values (Mode I) at initial crack growth are in good agreement with the $\text{j}{}_{\mathrm{IIIC}}$ values (Mode III). In addition, the effect of unloading on fracture toughness is examined.     

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.     

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.     

Fracture toughness and fracture energy measurements on aluminium alloys

Methods of conducting and analysing instrumented Charpy impact tests have been discussed and applied in measuring the initiation fracture toughness, $\text{K}{}_{\mathrm{Ic}}$, of two precipitation hardened Al-alloys.For full speed impact tests a method for indirectly deriving fracture load from “system stiffness” and “time to fracture” has been found to be the most suitable. In the lower speed impact tests measured fracture load has been used directly to calculate $\text{K}{}_{\mathrm{Ic}}$ In these tests an energy method superficially resembling “specific surface energy” has also been used to calculate $\text{K}{}_{\mathrm{Ic}}$.     

Characterization of transition temperature behavior of HY130 steel by the JIc fracture toughness parameter

The objectives of this study were to determine whether the $\text{J-R}$ curve approach could be used to evaluate the ductile to brittle temperature performance of a high yield strength structural steel (HY130) and to demonstrate that the single specimen unloading compliance method is applicable to evaluate $\text{J}{}_{\mathrm{Ic}}$ values and $\text{J-R}$ curves for compact specimens tested at temperatures from ?192 to 150°C. The major conclusions of this work are that $\text{J}{}_{\mathrm{Ic}}$ and the complete $\text{J-R}$ curve can be obtained using the single specimen method over the above temperature range and that $\text{J}{}_{\mathrm{Ic}}$ does define a ductile to brittle transistion temperature for HY130 steel which should be more valuable for structural design than that found from Charpy $\text{V}$ or dynamic tear specimens because it is based on a fracture toughness parameter. The comparison of the ${}_{\mathrm{Ic}}$ transition temperature and that from Charpy $\text{V}$ specimens shows that the Charpy $\text{V}$ transition temperture is more conservative for the HY130 steel tested. In transitional $\text{J}{}_{\mathrm{I}}$ specimens which demonstrated a ductile crack tearing followed by a brittle failure, scanning microscope stereo pair fractography showed that the transition from ductile to brittle behavior was very gradual in comparison to the distinct crack tips obtained on ductile specimens broken in a brittle fashion at a cryogenic temperature.     

Some problems in experimental fracture mechanics

A standard procedure for the determination of fracture toughness K_IC is discussed. The insufficiency of the existing K_ic determination confidence criteria is stressed and the following criteria are proposed instead: φ_max ? 1.5%; $\text{σ}{}_{\mathrm{fr}}{}^{\mathrm{net}}\text{σ}{}_{\mathrm{0.2\; ?\; 0.8}}$, in conjunction with the old criterion $\text{P}{}_{\max }\text{P}{}_{\mathrm{Q}}\text{? 1.1}$. Determination of K_IC from P_max should be used instead of from P_Q.A method for the determination of a point on the “force-displacement” diagram corresponding to crack growth initiation is set forth. The method is based on specimen compliance tests under repeated load-relief cycles. The crack growth initiation point is used to determine both the critical crack opening and plane strain fracture toughness. The indefinite effect of the growing crack (in the ease of crack opening or Cherepanov-Rice integral calculations) is thereby eliminated. Necessity is emphasized to determine the share of the J-integral which contributes to fracture process. A method for plotting the elastic displacement diagram is proposed which allows on the basis of preliminary estimates to determine fracture toughness of small-sized specimens without using special setups. The area ratio between the plastic and elastic strain diagrams is proposed to be adopted as fracture type criterion. Certain experiments to determine crack resistance of material specimens are described and discussed.     

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.