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.     

Study of the relationship between fracture toughness (J IC) and bulge ductility

A theoretical model relating fracture toughness expressed as J _IC and bulge ductility {ie71-1} for a material exhibiting linear elastic behavior at low temperature and elastic-plastic behavior at higher temperatures is proposed. This model shows a variation of J _IC with {ie71-2} for linear elastic behavior and J _IC with {ie71-3} for elastic-plastic behavior. The model contains three constants to be determined experimentally for a given material, specimen geometry and testing conditions. A case study on 1045 steel in the temperature range ?60 to 25°C confirms the validity of the model. The experimental results help in determining the size of the fracture zone ahead of the crack as well as the mechanisms for crack blunting and crack growth.     

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.     

An alternative formulation of the Ritchie-Knott-Rice local fracture criterion

In the paper an alternative formulation of the RKR local fracture criterion is proposed. It is based on the features of the stress distribution in front of a blunted crack in an elastic-plastic material. The stress distribution is computed using the finite strain option in the finite element method. It is postulated that the opening stress in front of the crack should be greater than the critical one, σ_c, over the distance l ? l_c, where l_c is considered as a material parameter. The hypothesis is applied to estimate the influence of the in-plane constraint on fracture toughness. New formulas to compute the critical value of the J-integral are derived both for the small scale yielding and large plastic deformations in front of the crack. The results obtained are compared with the Sumpter and Forbes experimental results and with the O’Dowd analytical formula concerning the J_c = J_c(J_IC,Q) relation.     

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.     

Comparison of various methods of measuring kic on small precracked bend specimens that fracture after general yield

An experimental investigation into the measurement of fracture toughness on small precracked bend specimens after general yield is described. Six parameters are compared on the basis of their accuracy and utility in predicting $\text{K}$_Ic. The parameters are: (i) the on-load crack tip opening displacement, COD, (ii) the lateral (notch root, crack tip) contraction, NRC, (iii) the angle of bend, (iv) the stretch zone, (v) the $\text{J}$ integral, and (vi) the equivalent energy. The materials used were. for the most part, A533B and 4340 steels.     

Upper shelf temperature dependence of fracture toughness for four low to intermediate strength ferritic steels

To examine the inadequacy and expose the potential consequences of utilizing transition temperature range fracture toughness values when performing fracture mechanics analyses on structures operating at upper shelf temperatures, the upper shelf fracture toughness behavior of three rotor forging steels (ASTM A471 NiCrMoV, ASTM A470 CrMoV and AISI 403 modified 12 Cr) plus an ASTM A217 $\text{2}\text{1}\text{4}\text{Cr}$-lMo cast steel was investigated. Elastic-plastic fracture toughness values were obtained via the $\text{J}{}_{\mathrm{IC}}$ resistance curve test technique. Except for the CrMoV rotor steel, upper shelf fracture toughness peaked near the temperature where zero percent brittle fracture first occurred in the Charpy V-notch impact tests after which decreases of 25–45% in toughness were realized. Fracture toughness tests were conducted up to 800°F.     

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 numerical and experimental investigation on the use of J-integral

Finite element analysis was used to determine numerically Rice's J-integral values in centrally notched plates of 4340 steel. These numerical values were compared with corresponding J-integral values using Dugdale model and antiplane strain model with a power law hardening of n = 0.3. J-integral was also computed for a crack extending into its own plastic yield region under constant loading. For increasing level of loading, σ, the rate of increase in J-integral decreases and J-integral remains almost constant at $\text{σ}\text{σ}{}_{\mathrm{YS}}\text{= 1}$ under such crack extension.A limited number of fracture tests were conducted with centrally notched 4340 steel specimens heat treated to yield strength levels of 150,180, 210 and 240 ksi. Fracture data showed that the critical J-integral, calculated and measured, is insensitive to crack tip sharpness for the lower strength 4340 material and thus the J_c fracture criteria appears suited in correlating fracture data.     

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.     

On the path independent integral-Ĵ

The path independent integral, $\text{J}\text{?}$, is presented as the rate of energy flux during crack extension. This integral is an extension of the J-integral proposed by Rice and includes the existence of a fracture process region and the effect of plastic deformations, body forces, thermal strains and inertial of material.It is shown that the $\text{J}\text{?}\text{-}\text{integral}$ can include as special cases other fracture mechanics parameters such as J by Rice, $\text{G}\text{?}$ by Eftis et al., J¹ by Blackburn or f by Strifors.A definition of the $\text{J}\text{?}\text{-}\text{integral}$ in a three-dimensional problem is presented and possibility of applying the $\text{J}\text{?}\text{-}\text{integral}$ as fracture criterion is discussed.     

Limitations of elastic definitions in Al-Si-Mg cast alloys with enhanced plasticity: linear elastic fracture mechanics versus elastic-plastic fracture mechanics

Linear elastic fracture mechanics describes the fracture behavior of materials and components that respond elastically under loading. This approach is valuable and accurate for the continuum analysis of crack growth in brittle and high strength materials; however it introduces increasing inaccuracies for low-strength/high-ductility alloys (particularly low-carbon steels and light metal alloys). In the case of ductile alloys, different degrees of plastic deformation precede and accompany crack initiation and propagation, and a non-linear ductile fracture mechanics approach better characterizes the fatigue and fracture behavior under elastic-plastic conditions.To delineate plasticity effects in upper Region II and Region III of crack growth an analysis comparing linear elastic stress intensity factor ranges (ΔK_el) with crack tip plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) is presented. To compute plasticity corrected stress intensity factor ranges (ΔK_pl), a new relationship for plastic zone size determination was developed taking into account effects of plane-strain and plane-stress conditions (“combo plastic zone”). In addition, for the upper part of the fatigue crack growth curve, elastic-plastic (cyclic J based) stress intensity factor ranges (ΔK_J) were computed from load-displacement records and compared to plasticity corrected stress intensity factor ranges (ΔK_pl). A new cyclic J analysis was designed to compute elastic-plastic stress intensity factor ranges (ΔK_J) by determining cumulative plastic damage from load-displacement records captured in load-control (K-control) fatigue crack growth tests. The cyclic J analysis provides the true fatigue crack growth behavior of the material. A methodology to evaluate the lower and upper bound fracture toughness of the material (J_IC and J_max) directly from fatigue crack growth test data (ΔK_FT(JIC) and ΔK_FT(Jmax)) was developed and validated using static fracture toughness test results. The value of ΔK_FT(JIC) (and implicitly J_IC) is determined by comparing the plasticity corrected elastic fatigue crack growth curve with the elastic-plastic fatigue crack growth curve. A most relevant finding is that plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) are in remarkably good agreement with cyclic J analysis results (ΔK_J), and provide accurate plasticity corrections up to a ΔK corresponding to J_IC (i.e. ΔK_FT(JIC)). Towards the end of the fatigue crack growth test (above ΔK_FT(JIC)) when plasticity is accompanied by significant tearing, the cyclic J analysis provides a more accurate way to capture the true behavior of the material and determine ΔK_FT(Jmax). A procedure to decouple and partition plasticity and tearing effects on crack growth rates is given.Three cast Al-Si-Mg alloys with different levels of ductility, provided by different Si contents and heat treatments (T61 and T4) are evaluated, and the effects of crack tip plasticity on fatigue crack growth are assessed. Fatigue crack growth tests were conducted at a constant stress ratio, R = 0.1, using compact tension specimens.     

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.     

Temperature dependence of fracture toughness J IC and ductility for BCC materials in the transition region

The temperature dependence of ductility, strength and fracture toughness for a BCC material undergoing predominantly linear elastic behavior at low temperatures and elastic-plastic behavior at higher temperatures is examined. A model, based on ductile fracture mechanisms involving void nucleation followed by cavity growth and void coalescence, is developed to relate the fracture toughness parameter J _IC with temperature. Two general equations for linear elastic and elastic plastic regimes of J _IC versus temperature T, are obtained. Applications of this model to experimental data obtained on a carbon steel show that J IC varies with T ² at low temperatures and with T at higher temperatures, thus defining a transition temperature.     

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.     

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.     

Numerical simulations to support the normalization data reduction technique

The normalization data reduction (NDR) technique is an analytical methodology for characterizing the upper shelf fracture toughness of steels in the ductile regime, both in terms of critical toughness (J_Ic) and resistance to ductile crack extension (J-R curve). It represents an alternative to the more commonly used multi-specimen or single-specimen (unloading compliance and potential drop) techniques.Finite element analyses of a growing crack are executed to evaluate the performance of the technique. This approach has the advantage to remove large uncertainties entailing experimental results. Results demonstrate the precision of the method.     

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.     

Size effect on the fracture toughness of metallic foil

The size effects on fracture behavior of Cu foil are investigated by a new optical technique, the digital speckle correlation method (DSCM). Displacement and strain fields around a crack tip are analyzed for different thicknesses of Cu foil. Then, the J integral and fracture toughness J _C are evaluated directly from the strain fields around the crack tip. The fracture toughness J _C is obtained as a function of foil thickness. The results indicate that J _C indeed depends on foil thickness within a certain range of thickness (the thickness varies from 20 micron to 1 millimeter in this work).     

Fracture toughness and crack morphology in indentation fracture of brittle materials

The relationship between the indentation fracture toughness, K _c, and the fractal dimension of the crack, D, has been examined on the indentation-fractured specimens of SiC and AIN ceramics, a soda-lime glass and a WC-8%Co hard metal. A theoretical analysis of the crack morphology based on a fractal geometry model was then made to correlate the fractal dimension of the crack, D, with the fracture toughness, K _IC, in brittle materials. The fractal dimension of the indentation crack, D, was found to be in the range 1.024–1.145 in brittle materials in this study. The indentation fracture toughness, K _c, increased with increasing fractal dimension, D, of the crack in these materials. According to the present analysis, the fracture toughness, K _IC, can be expressed as the following function of the fractal dimension of the crack, D, such that $$In K_{IC} = {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\{ In[2\Gamma E/(1 - \nu ^2 )] - (D - 1)In r_L \}$$ Where Γ is the work done in creating a unit crack surface, E is Young's modulus, v is Poisson's ratio, and r _L is r _min/r _max, the ratio of the lower limit, r _min, to the upper limit, r _max, of the scale length, r, between which the crack exhibits a fractal nature (r _min ?r?r _max). The experimental data (except for WC-8%Co hard metal) obtained in this study and by other investigators have been fitted to the above equation. The factors which affect the prediction of the value of K _IC from the above equation have been discussed.