Static Stress Intensity Research Articles

Dynamic fracture of unidirectional graphite fiber composite strips

An approximate equation of motion is derived and is used in the analysis of a dynamically propagating crack in a highly orthotropic fiber composite infinite strip subjected to constant displacement Mode I loading. With the use of Fourier transforms, the problem is reduced to an equation which is solved by the Wiener-Hopf technique. The dynamic stress intensity factor is derived and is expressed as the product of a velocity correction factor and a static stress intensity factor. The corresponding dynamic energy release rate is derived also and it is found not to be explicitly dependent upon the crack-tip velocity. It is found experimentally that the long strip configuration subjected to constant extensional displacement can simulate constant crack propagation velocities. Accordingly, the model's dynamic energy release rate is used to determine the dynamic fracture energy (toughness) of 90° Hercules AS/3501-6 graphite epoxy composites.

Impacted Notch Bend Specimens

The proposed test procedure for instrumented impact testings is evaluated by the experimental and numerical dynamic fracture results obtained for Homalite-100, polycarbonate, A533B steel and 6061 aluminum notched bend specimens. As expected, brittle fracture of the polymeric, steel and aluminum impacted notch bend specimens considered in this paper cannot be predicted by the static stress intensity factors at the instant of crack propagation. The fracture energy was only a fraction of the total energy and was equally unsuitable for dynamic fracture characterization of these specimens. This evaluation suggests that despite the enormous correlation studies which justify the use of static analysis for specific specimens under specified loading conditions, the proposed procedure should not be used to evaluate fracture data of impacted notch bend specimens of other configurations and loading rates.

Static finite element stress intensity factors for annular cracks

Results of finite element static stress intensity factor calculations for an annular crack around a spherical inclusion (void) are presented and compared with those from approximate analytical methods.

Propagation and arrest of an edge crack in a semi-infinite solid

The reflectionless stress intensity factor is determined for an edge crack in a semi-infinite solid, subject to various applied loadings. By comparing its value with that of the static stress intensity factor, the simple KIa crack arrest procedure is shown to be conservative for this particular situation, in that it over-predicts the crack arrest length. The results are discussed in relation to the water-cooled reactor pressure vessel LOCA problem, which is currently analyzed via the ASME Section XI Code provisions, which are based on the KIa approach.

Fracture of WC-Co alloys: an example of spatially constrained crack tip opening displacement

This paper attempts, both experimentally and theoretically, to account quantitatively for the propagation of cracks in WC-Co alloys. Evidence is presented which shows that cracks propagate through the ductile Co phase. It is further shown that the square of the quasi static stress intensity factor (KIC) of a slowly propagating crack is linearly related to the Co mean free path. On the assumption that crack tip plasticity cannot extend beyond a single interlayer of Co it is found that the yield stress must be close to twice the theoretical shear stress of Co. Thus, for a particulate composition which consists of grains sufficiently resistant to cleavage and plastic yield, and is bonded by a matrix which is ductile and not susceptible to cleavage,KICcan be calculated. It therefore appears possible, for the first time, to predict accurately from first principles, the fracture toughness of a real elastic-plastic body.

Static and Dynamic Stress Intensity Factors by the Method of Transmitted Caustics

The stress intensity factors in plexiglas plates containing an edge crack and subjected to static or dynamic loading are determined by the optical method of caustics. Measurements of the applied load were accomplished by means of a piezoelectric transducer and the caustics obtained in the experiments were photographed during the process of loading by using a Cranz-Schardin high speed camera. It has been found that the stress intensity factors for a dynamic loading are always higher than the corresponding stress intensity factors for a static loading of the same magnitude.

Dynamic stress intensity factors for arresting cracks in DCB specimens

The crack arrest experiments were performed in wedge-loaded DCB specimens (321x127x10 mm) made from an epoxy resin (Araldit B). Notches with different root radii were used to achieve different initial crack velocities. Dynamic stress intensity factors for propagating and subsequently arresting cracks were determined using the shadow spot method of Manogg [3] in combination with a Cranz~Schardin high speed camera; the static stress intensity factors for the corresponding crack lengths were obtained using the conventional stress intensity factor formulae from deflection measurements at the loading point. Experimental results for cracks, initiated at different values of the stress intensity factor at initiation (KI_) and thus propagating at different initial crack velocities, are summarized indFig, i. Fig. la shows values of the dynamic stress intensity factor KIyn (experimental points in the upper part of the diagram) as a function of crack length a compared with the corresponding static stress intensity factor K~ tat curve. The measured velocities are given in the lower par t of the diagram additionally. The same results as in Fig. la, but plotted in a different form, are shown in Fig. lb. Simplified curves have been drawn through the measured data points. The very early phase,of crack propagation (dashed lines), being of less importance in this context, has not been investigated. The following characteristics of the crack arrest process can be drawn from Figs. la and Ib: i. At the beginning of the crack propagation phase the dynamic stress intensity factor K~ yn is smaller than the corresponding static value K~ tat. At the end of the crack propagation phase the dynamic stress intensity factor K~yn is larger than the corresponding static value K~ tat. Only after arrest does the dynamic stress inten

Crack branching in Homalite-100 sheets

Crack branching in Homalite-100 sheets of 1/8-in. and 3/8-in. thickness was studied by dynamic photoelasticity. Dynamic stress intensity factors, crack velocities and branching angles were measured and corresponding static stress intensity factors were determined by the method of finite element analysis. Dynamic stress intensity factors which preceded the actual branching reached a peak value of approximately three times the fracture toughness. The dynamic stress intensity factor drops prior to branching and then increases again to the maximum stress intensity factor at which point branching could occur again. Roughness of the fracture surface can be related to large dynamic stress intensity factors and crack velocities prior to branching and also after branching. Average branching angle was 26 deg. The results of this series of tests thus suggest that large dynamic stress intensity factors are necessary but not sufficient to cause crack branching.

Ni-Cr-Moマルテンサイト鋼の水中疲労き裂伝ぱ則

The effect of delayed failure on the fatigue crack propagation rate in water of Ni-Cr-Mo martensitic steel was investigated. The results obtained are as follows:(1) The relation between the fatigue crack propagation rate da⁄dN in air and the stress intensity factor range ΔK is expressed as da⁄dN=C1(ΔK)m1, and m1 increases with increase of Km⁄ΔK, where Km is the mean stress intensity factor.(2) The relation between the crack propagation rate da⁄dt in delayed failure and the static stress intensity factor KD is expressed as da⁄dt=C2(KD)m2.(3) The fatigue crack propagation rate (da⁄dN)w in water is expressed as the addition of both fatigue crack propagation rate in air and crack propagation rate in delayed failure, and the following equation holds:(This article is not displayable. Please see full text pdf.) where f is the frequency (cpm); β is a coefficient of addition and depends mainly on f and Km⁄ΔK. Under the condition in this experiment (f=55∼345 cpm, Km⁄ΔK=0.5∼4), β is 0.2∼0.4.(4) Physical meaning of β is considered to be the ratio of the time in which the tri-axial tensile stress state region at the crack tip meet a cluster of hydrogen atoms during one cycle.

Environmentally Controlled Fatigue Crack-Growth Rates in SAE 4340 Steel—Temperature Effects

The temperature dependence of sustained-loading and corrosion-fatigue crack-propagation behavior of SAE 4340 steel immersed in distilled water was investigated using the fracture mechanics approach. During the load cycle, stress-intensity histories had values higher than the static threshold stress intensity (KIscc). For a stress-intensity range of 20 ksi in., a factor of 30 increase in the corrosion-fatigue crack-growth rate was noted for a temperature increase of 70 deg C. The mechanical variables were found to have much less influence than the environmental reaction rate. In contrast with dry air results, the fatigue crack-growth rate in a distilled water environment was dependent on the mean stress-intensity for stress-intensity histories above KIscc. This dependence varied with temperature level.

Environmentally Assisted Fatigue Crack Growth Rates in SAE 4340 Steel

Corrosion fatigue crack growth rates for SAE 4340 steel in distilled water environments were investigated utilizing fracture mechanics techniques. Crack growth rates, resulting from various forms of repeated loading, were compared to those induced by static load using small sample statistical theory. These comparisons indicate that corrosion fatigue crack growth may be either time or cycle dependent depending on the load profile, loading frequency, and temperature. Data are presented suggesting that whenever the maximum cyclic stress intensity in the fatigue cycle is below the static threshold stress intensity (KIscc), the environment no longer plays a major part in assisting the crack growth rate.

Effect of vibration on the creep of tensile-test specimens of the aluminum alloy Al−Mg−Si (PA-4)

In this work are presented the results of research on vibrational creep at normal temperature of an aluminum alloy containing magnesium and silicon (designated PA-4). A uni-directional positive load is applied to a tensile-test specimen, such that the stress intensity in the specimen is of the type\(\sigma (t) = \sigma _m (1 + Asin\omega t)\) whereσ m is the mean (static) stress intensity andA =σ a /σ m is the ratio of the vibratory-stress intensity to the mean intensity. The results are given in the form of families of curves of plastic (i.e., permanent) deformation for various values ofA, namely,A=0.0000, 0.0065, 0.05500, 0.1000 and 0.2000.