Plastic Collapse Stresses for Pipes With Inner and Outer Circumferential Cracks

Bending stresses at incipient plastic collapse for pipes with circumferential surface cracks are predicted by net-section stress approach. Appendix C-5320 of ASME B&PV Code Section XI provides an equation of bending stress at the plastic collapse, where the equation is applicable for both inner and outer surface cracks. That is, the collapse stresses for pipes with inner and outer surface cracks are the same, because of the pipe mean radius at the cracked section being entirely the same. Authors considered the separated pipe mean radii at the cracked ligament and at the uncracked ligament. Based on the balances of axial force and bending moment, equations of plastic collapse stresses for both inner and outer cracked pipes were developed. It is found that, when the crack angle and depth are the same, the collapse stress for inner cracked pipe is slightly higher than that calculated by the Appendix C equation, and the collapse stress for outer cracked pipe is slightly lower than that by the Appendix C equation, as can be expected. The collapse stresses derived from the three equations are almost the same in most instances. However, for less common case where the crack angle and depth are very large for thick wall pipes, the differences among the three collapse stresses become large. Code users pay attention to the margins of plastic collapse stresses for outer cracked pipes, when using Appendix C equation.

Residual Stress State in Single-Edge Notched Tension Specimen Caused by the Local Compression Technique

Three-dimensional (3D) finite element analyses (FEA) are performed to simulate the local compression (LC) technique on the clamped single-edge notched tension (SE(T)) specimens. The analysis includes three types of indenters, which are single pair of cylinder indenters (SPCI), double pairs of cylinder indenters (DPCI) and single pair of ring indenters (SPRI). The distribution of the residual stress in the crack opening direction in the uncracked ligament of the specimen is evaluated. The outcome of this study can facilitate the use of LC technique on SE(T) specimens.

T-Stresses for Edge Cracks and Vanishing Ligaments

An edge-cracked half-plane 0 < x < A and a half-plane x > 0 with a semi-infinite crack x > a perpendicular to the edge are examined in this paper. Uniform crack-face loading is thoroughly examined, with a thorough exposition of the Koiter Wiener–Hopf approach (Koiter, 1956, “On the Flexural Rigidity of a Beam Weakened by Transverse Saw Cuts,” Proc. Royal Neth. Acad. of Sciences, B59, pp. 354–374); an analytical expression for the corresponding T-stress is obtained. For the additional cases of (i) nonuniform edge-crack crack-face loading σ(x/A)k (ℜ(k)>-1), (ii) concentrated loading at the edge-crack crack mouth, the Wiener–Hopf solutions and analytical T-stress expressions are provided, and tables of T-stress results for σ(x/A)k and σ(1-x/A)k are presented. A Green's function for the edge-crack T-stress is developed. The differing developments made by Koiter (1956, “On the Flexural Rigidity of a Beam Weakened by Transverse Saw Cuts,” Proc. Royal Neth. Acad. of Sciences, B59, pp. 354–374, Wigglesworth (1957, “Stress Distribution in a Notched Plate,” Mathematika, 4, pp. 76–96), and Stallybrass (1970, “A Crack Perpendicular to an Elastic Half-Plane,” Int. J. Eng. Sci., 8, pp. 351–362) for the case of an edge-cracked half-plane are enhanced by deducing a quantitative relationship between the three different Wiener–Hopf type factorizations. An analytical universal T-stress expression for edge-cracks is derived. Finally, the case of a vanishing uncracked ligament in a half-plane is examined, and the associated Wiener–Hopf solution and analytical T-stress expression are again provided. Several limiting cases are examined.

Evaluation of Dynamic J-R Curve by Using Normalization Method for Long Crack Extension

The test method for the reliability of this research dynamic J-R curve for long crack extension based on normalization method was introduced on this research. For nuclear power plant piping material made of ferritic steel, dynamic J-R curve is one of the important material properties used to evaluate the integrity for piping with the critical leakage crack size under seismic loading such as earthquake loading on leak before brake design (LBB). The measurement of dynamic J-R curve by compliance method is very difficult due to the fast loading speed. Normalization method of ASTM E1820 code A15 is therefore often used because of the merit that J-R curve can be obtained by only using load–displacement curve without measuring the crack extension length during the test. However, there is a restriction that physical crack extension should not exceed the lesser length of 4mm or 15% of the initial uncracked ligament. For J-T analysis on LBB design, long crack extension data on J-R curve are needed to simulate the crack stability of long cracked piping corresponding to leakage rate of 10gpm. In this paper, to overcome this problem at applying for the normalization method, two specimens were used where one is for short crack extension and the other is for long crack extension. Utilizing the two test data, dynamic J-R curve over the crack extension length range designated to ASME code was estimated.

Fracture Mechanisms of Bone: A Comparative Study between Antler and Bovine Femur

ABSTRACTIn this study, fracture toughness of North American elk (Cervus elaphus canadensis) antler and bovine femur were measured using four-point bending tests on single-edge notched compact samples (ASTM C1421). Tests were conducted on crack growth directions longitudinal and transverse to the long axis of antler and bone in both dry and hydrated conditions to study the effects of fiber orientation and hydration. Fracture toughness results in the transverse orientation were much higher than that in the longitudinal orientation and increased with degree of hydration for both antler and bovine femur. The fracture toughness of antler was ∼ 50% higher than that of bovine femur. The highest fracture toughness value was obtained from the hydrated antler in the transverse orientation, which reached 10.31 MPa·m1/2 compared to that measured from bovine femur, which was 6.35 MPa·m1/2. The crack propagation and fracture surface were characterized using scanning electron microscopy. Toughening mechanisms, including crack deflection by osteons, uncracked ligament bridging, and microcracks formation, are observed and discussed. Comparisons between antler and bone are made.

Fracture mechanics in the creep range

Cracked high temperature components may fail by crack growth, net-section rupture, or some combination of both processes. This paper reviews the fracture mechanics concepts required to describe this behaviour. Procedures are presented for evaluating relevant characterizing parameters using experimental, numerical and limit analysis methods. Models for predicting crack propagation rates from uni-axial creep data involving ductility exhaustion in a process zone at a crack tip are outlined. Both the influence of build-up of damage in the process zone and material deterioration in the uncracked ligament are considered. It is shown that the models give satisfactory correlations with experimental data.

Influence of net section damage on creep crack growth

Fracture mechanics concepts for describing creep crack growth in terms of ductility exhaustion in a process zone at the crack tip are reviewed and extended to include damage accumulation in the ligament ahead of a crack. Applications are considered which show that net section damage has most influence for short cracks and plane stress conditions where significant damage can develop in the uncracked ligament. It is shown that, under plane strain loading, insufficient ligament damage occurs during the crack growth phase for it to have an appreciable effect on failure times. A method is also presented for accounting for the influence of an incubation period prior to the onset of cracking and for making residual life estimates.

J-Integral Analysis of Three-Point Bend Specimen

A J-integral solution is derived for the three-point bend [SE(B)] specimen. The solution allows analysis for a/W greater than 0.2. The solution is based on an approach that does not require an assumption of net-section yielding in the remaining uncracked ligament. Solutions are presented for both the deformation theory J and modified J. These solutions are suitable for J-resistance curve analysis and require data from only one specimen. Solution for a special case of power law hardening material is presented. Consequences of the separability assumption between load-point displacement and crack length on the resulting J solution are discussed. This work indicates that the plastic η factor from previous solutions is significantly underestimated for a/W less than 0.6. Numerical results show that Jd and JM resistance curves are closer than those obtained from previous solutions. A solution for normalizing the load-displacement curve is also presented.

The fracture of wood in tension parallel to the grain

The fracture of commercial Hem-Fir boards in the LR and LT modes was studied, using both saturated and air-dry specimens. Notched samples were tested in flexure (third-point loading). It was found that the concepts of linear elastic fracture mechanics could be applied, even when the crack extension was in a direction perpendicular to the initial notch. However, the physical interpretation of the apparent fracture toughness, [Formula: see text], remains unclear. It was also found that the apparent flexural stsrength increased as the size of the uncracked ligament decreased. Finally, the results indicated that both the nominal flexural strength and the fracture toughness were greater for the saturated specimens, probably due to an increase in viscoelastic behaviour at high moisture contents.