Approximate Mode II velocity correction factors for 90° unidirectional fiber composites

A static Mode III isotropic/Mode II orthotropic analogy is developed for 90° highly orthotropic fiber composites. This static analogy is extended to the dynamic regime and the velocity correction factors for the dynamic energy release rate and the dynamic stress intensity factor are obtained for the Mode II case. The complete dynamic analogies are given. The approximate Mode II 90° velocity correction factors $\text{W}{}_{\mathrm{II(90°)}}$ and $\text{S}{}_{\mathrm{II((90°)}}$ are of the same general form as the approximate Mode I velocity correction factors, $\text{W}{}_{\mathrm{I(0°)}}$, $\text{W}{}_{\mathrm{I(90°)}}$, $\text{S}{}_{\mathrm{I(0°)}}$ and $\text{S}{}_{\mathrm{I(90°)}}$ Whereas the four Mode I velocity correction factors approach zero as the crack-tip velocity approaches the composite shear wave speed, $\text{w}{}_{\mathrm{II(90°)}}$ and $\text{s}{}_{\mathrm{II(90°)}}$ approach zero as the crack-tip velocity approaches the larger extensional wave speed.     

The dependence of mode III fracture initiation toughness on strength and microstructure

HF1, a hypereutectoid steel which is high in silicon and manganese content, was selected to examine the dependency of Mode III fracture initiation toughness $\text{(K}{}_{\mathrm{IIIQ}}\text{)}$ on microstructure and strength. Four heat treatments of this steel were investigated and results were compared with those previously reported on a hypoeutectoid steel (4340). It was found that $\text{K}{}_{\mathrm{IIIQ}}$ is independent of strength and depends only on microstructure and other metallurgical factors. The $\text{K}{}_{\mathrm{IIIQ}}$ value of the hypereutectoid steel and for the nucrostructures examined varied between 35 and 45 MPa.√m. In the higher strength specimens, an initial Mode III crack extension was followed by Mode I crack branching.     

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.     

Experimental determination of Jc data using different types of specimen

$\text{J}{}_{\mathrm{c}}$ values for two medium-strength steels have been experimentally determined from tests on different types of specimen. Evaluation of test records was performed utilizing a digital computer. Two independent electrical methods were employed to determine critical points. Results indicate independence of $\text{J}{}_{\mathrm{c}}$ on specimen configuration and hence support the suggestion that the $\text{J-}\text{integral}$ be a relevant parameter for onset of crack growth. Present results compare favourably with previously published data.     

Fracture of round bars loaded in mode III and a procedure for KIIIc determination

The available literature reports few studies on Mode $\text{III}$ fracture. In fact, even though the Mode $\text{III}$ fracture toughness, $\text{K}{}_{\mathrm{IIIc}}$ is an important factor in design and analysis of fractures under torsional loading, the procedure for the measurement of $\text{K}{}_{\mathrm{III}}$ is yet to be standardized.In this paper, the results of a simple analysis, which determines the displacement produced by the size dependent plasticity and the growth of crack in a circumferentially cracked round bar subjected to Mode $\text{III}$ loading, are presented. It is shown that plastic zone size decreases as bar diameter increases. This implies that whereas a small diameter bar can fail in a ductile manner, a large diameter bar may undergo a predominantly linear, elastic and brittle fracture even though the material is ductile.The analytical results are verified by experimental measurements on circumferentially cracked specimens loaded in Mode $\text{III}$. Based on this, one can determine the limiting value of the bar diameter, which must be tested to obtain a $\text{K}{}_{\mathrm{IIIc}}$ in a predominantly linear elastic condition. Further, a new and simple procedure for the determination of $\text{K}{}_{\mathrm{IIIc}}$ is proposed. This procedure enables one to determine the stress intensity factor at which a crack starts extension in the specimen under Mode $\text{III}$ loading.     

Mixed mode stress intensity distributions for part circular surface flaws

Using the frozen stress method, mixed mode stress intensity factor (SIF) distributions were obtained for a series of low aspect ratio part circular surface flaws in flat plates over a depth to plate thickness range of 0.20–0.70. Mode I results were compared with Mode I solutions in order to sense the influence of the crack surface inclination to the free boundary. It was found that maximum SIF values did not necessarily occur at maximum flaw depth. A rationale is offered to explain this observation. It was also found that the effect of the boundary inclination was to reverse the relative magnitudes of $\text{K}{}_1\text{K}\text{?}{}_1$ and $\text{K}{}_2\text{K}\text{?}{}_2$ in going from a 30° to a 60° crack surface inclination with the boundary.     

An investigation of the blunting line

Experimental evidence obtained on 3-point SENB specimens of carbon steel (St52-3) is used to compare ways of determining the slope of the “blunting line” in $\text{J}{}_{\mathrm{Ic}}$ testing. The results demonstrate that the slope of the blunting line obtained by the stretched zone width (SZW) method is steeper than the blunting line predicted by the ASTM method. This results in lower values for both $\text{J}{}_{\mathrm{Ic}}$ and $\text{(Δa)}{}_{\mathrm{c}}$ as determined with the SZW method, compared with those obtained by the ASTM method. The increased conservatism compared to the ASTM approach and the experimental evidence underlying it recommend the SZW method for further study. The subsequent widespread use expected for any recognized $\text{J}{}_{\mathrm{Ic}}$ determination seems to justify the additional effort and expenses associated with the SZW method.     

On the influence of rubbing fracture surfaces on fatigue crack propagation in mode III

Fatigue crack growth has been studied under fully reversed torsional loading (R = ?1) using AISI 4340 steel, quenched and tempered at 200°, 400° and 650°C. Only at high stress intensity ranges and short crack lengths are all specimens characterized by a microscopically flat Mode III (anti-plane shear) fracture surface. At lower stress intensities and larger crack lengths, fracture surfaces show a local hill-and-valley morphology with Mode I, 45° branch cracks. Since such surfaces are in sliding contact, friction, abrasion and mutual support of parts of the surface can occur readily during Mode III crack advance. Without significant axial loads superimposed on the torsional loading to minimize this interference, Mode III crack growth rates cannot be uniquely characterized by driving force parameters, such as ΔK_III and ΔCTD_III, computed from applied loads and crack length values. However, for short crack lengths (?0.4 mm), where such crack surface interference is minimal in this steel, it is found that the crack growth rate per cycle in Mode III is only a factor of four smaller than equivalent behaviour in Mode I, for the 650°C temper at $\text{ΔK}{}_{\mathrm{III}}\text{= 45 MPa m}\text{1}\text{2}$.     

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 behavior of 4340 steel under mode III loading

An experimental investigation was conducted to examine how the upper stress intensity factor in parallel shear $\text{K}{}_{\mathrm{IIIQ}}$ (similar to $\text{K}{}_{\mathrm{IQ}}$ for Mode I) is affected by increasing the tensile strength of a material. Round notched and precracked bar specimens, fabricated from 4340 steel were used for the investigation. Based on results from four different heat-treatments of this steel it was found that the stress intensity factor $\text{K}{}_{\mathrm{IIIQ}}$ increases as the tensile strength increases. Values of $\text{K}{}_{\mathrm{IIIQ}}$ obtained for high strength 4340 steel are in agreement with those found by other investigators.     

Growth of Ca3Fe2Ge3O12 and Ca3Fe(Al,Cr) Ge3O12 garnets in molten bismuth germanate glasses

Additions of Fe₂O₃ to CaO·Bi₂O₃·2 GeO₂ cause Ca₃Fe₂Ge₃O₁₂ garnets to precipitate from the resultant melt at 1250°C. Garnets with the composition Ca₃Fe(Al, Cr) Ge₃O₁₂ are also precipitated by adding either $\text{Al}{}_2\text{O}{}_3\text{Fe}{}_2\text{O}{}_3$ or $\text{Cr}{}_2\text{O}{}_3\text{Fe}{}_2\text{O}{}_3$ mixtures. The well-formed crystals range from several to 100 μm in size and are obtained in 50 to 70% yields at $\text{Fe}\text{Bi}\text{= 0.4}$. Additions of Fe₂O₃ (up to $\text{Fe}\text{Bi}\text{= 1.0}$) to compositions containing ZnO, CdO, SrO, and BaO yield only dark glasses. The physical properties of these glasses suggest that Fe(III), in contrast to AL(III) & Ga(III), prefers octahedral coordination.     

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.     

Concentration quenching of Tb3+ luminescence in LaOBr and Gd2O2S phosphors

The concentration quenching of trivalent terbium ${}^5\text{D}{}_{\mathrm{3,4}}\text{→}{}^7\text{F}{}_{\mathrm{J}}$ emissions from UV-excited (La, Tb) OBr and (Gd, Tb)₂O₂S phosphors was studied. The activation concentration x was varied from 5·10^?5 to 0.2 for (La_1?xTb_x) OBr and from 10^?3 to 0.1 for (Gd_1?xTb_x)₂O₂S. ${}^5\text{D}{}_3\text{→}{}^7\text{F}{}_{\mathrm{J}}$ emissions (blue) were observed to quench first and the Tb³⁺ concentration giving rise to maximum intensity was 0.003 in (La, Tb) OBr and between 0.005 and 0.01 in (Gd, Tb)₂O₂S. The optimum concentration for ${}^5\text{D}{}_4\text{→}{}^7\text{F}{}_{\mathrm{J}}$ (green) emissions was 0.05 in (La, Tb) OBr and 0.03 in (Gd, Tb)₂O₂S. Dipole-dipole and dipole-quadrupole interactions are possible mechanisms for the quenching of emissions from the ⁵D₃ and ⁵D₄ levels.A method for determining the Tb³⁺ concentration in these phosphors, based on the intensity ratios of the ${}^5\text{D}{}_3\text{→}{}^7\text{F}{}_{\mathrm{J}}$ and ${}^5\text{D}{}_4\text{→}{}^7\text{F}{}_{\mathrm{J}}$ transitions, is also presented.     

Modified manjoine WOL specimen for JIc and δi tests

A procedure is presented by which a modified WOL specimen can be designed to withstand the load required to achieve a $\text{δ}{}_{\mathrm{i}}$, or $\text{J}{}_{\mathrm{Ic}}$ test for a low yield strength, high toughness material, using information from the test of a standard WOL specimen that has suffered plastic collapse of its loading arms. The $\text{K-}\text{calibration}$ for the family of geometries used is obtained from published data fitted to a 2-dimensional half-power series, and the load point and guage point compliances are obtained through a connected beam model that is calibrated from existing compliance data to imitate a WOL specimen. Prom these calibrations the $\text{J-}\text{integral}$ tensile component correction factor is evaluated and found to be applicable for this type of specimen.     

Photoelastic analysis of practical mode I fracture test specimens

A photoelastic technique for the evaluation of the isochromatic fringe patterns of practical Mode I fracture test specimen is presented.The new procedure uncouples the expressions for the stress intensity factor $\text{K}$ and the non-singular stress term $\text{A}$ from the governing maximum shear expression by employing a line perpendicular to the crack-tip in a photoelastic specimen, (this line intersects the isochromatic fringes at the locus of points $\text{r}{}_{\mathrm{i}}$, $\text{θ}{}_{\mathrm{i}}\text{= π/2}$, $\text{i = 1,2,…, n}$, where $\text{n}$ is the maximum analizable fringe) in developing the least-squares technique employed in this research.The least-squares expressions developed required no assumption of initial values for the stress intensity factor $\text{K}$ and the non-singular stress term $\text{A}$. The accuracy of the approach is then demonstrated by obtaining the $\text{K}$ and $\text{A}$ values of some practical Mode I specimens under applied uniaxial and biaxial stresses.     

The effect of loading pattern on crack growth instability under small-scale yielding conditions

A theoretical analysis shows that if a plane strain crack is stable up to a certain $\text{J}$ level ($\text{J}{}_{\mathrm{ST}}$) under small-scale yielding conditions and the displacement control loading conditions that are characteristic of a machine loaded specimen, then unstable fracture under load control conditions cannot occur at $\text{J}$ levels that are appreciably less than $\text{J}{}_{\mathrm{ST}}$. The results, therefore, give added confidence to the use of linear elastic fracture mechanics data, for assessing the integrity of cracked engineering structures with regard to catastrophic fracture.     

Application of the ac potential drop technique to the determination of R curves of tough ferritic steels

The suitability of the AC potential drop (ACPD) technique for detecting crack initiation and monitoring crack extension during slow stable growth has been investigated using side-grooved Charpy size specimens tested in three point bending. For ferritic steels with widely differing initiation and growth characteristics, the potential drop (PD) vs clip gauge opening displacement (CGOD) trace shows consistent behaviour, the most important feature being the occurrence of a minimum around the point of crack initiation. At low current frequency (150 Hz), there is close agreement between $\text{δ}{}_{\min }$, the COD corresponding to the minimum of the PD/CGOD trace and $\text{δ}{}_{\mathrm{i}}$ estimated by the recommended multispecimen technique for $\text{δ}{}_{\mathrm{i}}$ ranging from 0.02 to 0.37mm. In steels with $\text{δ}{}_{\mathrm{i}}$ less than about 0.1 mm, the minimum occurs at the same value of δ for both low (150 Hz) and high (4.7 kHz) frequencies. However, for steels with higher toughness, the minimum shifts to lower δ values as the frequency is increased. It appears that for any steel, there is a maximum frequency below which the minimum corresponds to $\text{δ}{}_{\mathrm{i}}$. It is demonstrated that the ACPD method can be employed to determine $\text{R}$ curves from single specimens.     

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 new method of determining JIc of steel by means of single specimen

A new method of determining $\text{J}{}_{\mathrm{Ic}}$ of medium to high strength steel by means of single TPB (three points bend) specimen is proposed and tested. Several kinds of steels with yield strength between 53 and 115 kg/mm² are tested. The calculations of each data set of a single specimen are carried out by computer. The results of single specimen method are in good agreement with those obtained by multi-specimen method.     

Fatigue crack growth rate under full yielding condition for 15CDV6 steel

Strain fatigue crack growth rate was studied using center cracked specimens for 15CDV6 steel tempered at 200°C after quenching by means of the method which deflections were controlled to a sloping load vs deflection line. Cyclic $\text{J-}\text{integral}$ values estimated from load vs deflection hysteresis loops are correlated with the growth rate. The relationship between them can be expressed by a simple power function $\text{da/dN = 2.5 × 10}{}^{\mathrm{?4}}\text{(ΔJ)}{}^{1.38}$ The plastic portion Δ$\text{J}{}_{\mathrm{p}}$ in $\text{J-}\text{integral}$ is exponentially increased as the deflection increases, while the peak value of the elastic portion Δ$\text{J}{}_{\mathrm{e}}$ appears as the deflection varies. These relations may provide a convenient way to use $\text{J-}\text{integral}$ in engineering practice. A concept is proposed that “high strain rate induces cleavage”. The critical value of the strain rate for the steel tested is 10^?4/sec. If the strain rate is higher than this value, cleavage predominates on the fracture surface. On the other hand, if it is lower than this value, dimples will prevail.