The fracture of wood under torsional loading

A series of experiments have been carried out on hardwood (red lauan) and softwood (sitka spruce) test pieces using static and cyclic torsional loading under displacement control. Measurements of the applied torque, the corresponding angle of twist and the number of cycles to failure were recorded. It was found that under static torsional loading, the strength of both hardwood and softwood reduced as the grain orientation of the sample to the axis of twist increased from 0° to 90° with a corresponding decrease of elastic modulus. Hardwood is stronger than softwood. In the fatigue test, when the torsional load is plotted against cycle number, the results showed that under displacement control stress relaxation occurs. The S–N curve for softwood has a shallower gradient than that of hardwood, indicating that the torsional strength of softwood is less affected by fatigue loading than hardwood. In both static and cyclic torsional loading tests, the failure mode of hardwood is slow and incomplete, whereas, softwood fails suddenly and completely. The crack growth is along the tangential direction in the hardwood cross-section and in the radial direction in the cross-section.     

A penny-shaped crack in a functionally graded piezoelectric strip under thermal loading

The mixed-mode thermoelectromechanical fracture problem for a functionally graded piezoelectric material (FGPM) strip with a penny-shaped crack is considered. It is assumed that the thermoelectroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under thermal loading. The crack faces are supposed to be insulated thermally and electrically. The thermal and electromechanical problems are reduced to singular integral equations and solved numerically. The stress and electric displacement intensity factors are presented for different crack size, crack position and material nonhomogeneity.     

Crack initiation and crack propagation under thermal cyclic loading

Theoretical and experimental investigations of crack initiation and crack propagation under thermal cyclic loading are presented. For the experimental investigation a special thermal fatigue test rig has been constructed in which a small circular cylindrical specimen is heated up to a homogeneous temperature and cyclically cooled down under well defined thermal and mechanical boundary conditions by a jet of cold water. At the end of the cooling phase the specimen is reheated to the initial temperature and the following cycle begins. The experiments are performed with uncracked and mechanically precracked specimens of the German austenitic stainless steel X6CrNi 1811.

In the crack initiation part of the investigation the number of load cycles to initiate cracks under thermal cyclic load is compared to the number of load cycles to initiate cracks under uniaxial mechanical fatigue loading at the same strain range as in the cyclic thermal experiment. The development of initiated cracks under thermal cyclic load is compared with the development of cracks under uniaxial mechanical cyclic load.

In the crack propagation part of the investigation crack growth rates of semi-elliptical surface cracks under thermal cyclic loading are determined and compared to suitable mechanical fatigue tests made on compact-tension and four-point bending specimens with semi-elliptical surface cracks. The effect of environment, frequency, load shape and temperature on the crack growth rate is determined for the material in mechanical fatigue tests.

The theoretical investigations are based on the temperature distribution in the specimen, which is calculated using finite element programs and compared to experimental results. From the temperature distribution, elastic and elastic-plastic stress distributions are determined taking into account the temperature dependence of the material properties. The prediction of crack propagation relies on linear-elastic fracture mechanics. Stress intensity factors are calculated with the weight function method and crack propagation is determined using the Paris relation.

To demonstrate the quality of the crack growth analysis the experimental results are compared to the prediction of crack propagation under thermal cyclic load.     

The investigation of crack growth in specimens with rectangular cross-sections under out-of-phase bending and torsional loading

The paper presents the fatigue test results of rectangular cross-section specimens made of 10HNAP (S355J2G1W) steel. The specimen height to width ratio was 1.5. The tests under bending with torsion were performed for the following ratios of bending to torsional moments M_aB/M_aT = 0.47, 0.94, 1.87 and the loading frequency 26.5 Hz. Nominal stresses were chosen for the equivalent stress according to the Huber-Mises hypothesis equal to 360 MPa. The tests were performed in the high cycle fatigue regime for the stress ratio R = −1 and phase shift between bending and torsion loading equal to ϕ = 0 and 90°. Crack initiation and propagation phases were observed on the specimen surface using the optical microscope (magnification 20×) with an integrated digital camera. The test results for the fatigue crack growth rate versus the stress intensity factor range for mode I and mode III have been described with the Paris equation.     

Fatigue crack growth of a welded tube–flange connection under bending and torsional loading

In this contribution the results of an experimental investigation into the fatigue crack growth of welded tube-to-plate specimens of steel StE 460 under bending, torsion, and combined in-phase and out-of-phase bending/torsion loading are presented. The tests were performed at stress ratios of R = −1 and R = 0. The residual stresses were reduced by thermal stress relief. The fatigue crack development is compared with the prediction on the crack growth rates of Paris. Individual stress intensity factors for the semielliptical surface cracks in the tube-flange specimens are approximated on a weight function analogy using the published solutions of other workers.     

A probabilistic model for fatigue crack growth under random loading

A model for predicting fatigue crack growth rate and life probabilistically under random load history is presented. It allows for random growth per cycle, and is based on experimental results of constant amplitude cyclic loads. Predictions of the model are on the conservative side at the same time avoiding overdesigning. The reliability is included in the model thereby avoiding the need for using a factor of safety or ignorance in estimating a fatigue life or a crack length after N cycles of load application. The model is computer-oriented.     

Conditions for crack kinking under stress-wave loading

Kinking of a crack in a prestressed body under the influence of incident stress waves is investigated on the basis of the balance of rates of energies. It is assumed that the crack tip will choose to propagate at a time, in a direction, and at a speed for which the energy flux into the propagating crack tip attains a maximum value with respect to variation of the kinking angle. It is shown that the balance of rates of energies implies that the crack tip speed is zero at the onset of fracture. Consequently, the conditions for the onset of crack kinking and for the computation of the kinking time and kinking angle are completely defined by the elastodynamic field around the original crack tip. Examples of the incidence of step stress waves on a semiinfinite crack in a prestressed body have been investigated. It is shown that for an incident antiplane wave with Mode III fracture, kinking is generally not possible. For an incident inplane wave with mixed Mode I–II fracture, kinking may happen. For that case curves are presented which relate the kinking time and the kinking angle to the state of prestress and to the parameters of the incident wave.     

A study of stress concentration zones under cyclic loading by thermal imaging method

A method is put forward for detection of stress concentration zones in structures under repeated cyclic loading. It is proposed that prior to cyclic loading the temperature characteristics of a structure should be stabilized, and then in the course of loading the temperature fields in the structure should be measured by instruments with subsequent analysis and processing of the thermograms. Translated from Problemy Prochnosti, No. 3, pp. 134–142, May–June, 2009.     

Flat crack under shear loading

Summary A solution is called complete when the explicit expressions are derived for the field of displacements as well as stresses in an elastic body. A new method is proposed here which allows us to obtain exact and complete solutions to various crack problems in elementary functions; no integral transforms or special function expansions are involved. The method is based on the new results in potential theory obtained earlier by the author. The method is applied to the case of a concentrated tangential loading of a penny-shaped crack. The main potential function and the relevant Green's functions are derived. An approximate analytical solution is obtained for a flat crack of general shape. A new set of asymptotic expressions is presented for the field of stresses and displacements near the crack tip in a transversely isotropic space. The use of the method is illustrated by examples.     

A non-conventional approach for crack problems in piezoelectric media under electromechanical loading

In this paper the elastostatic solution of an inclined crack problem has been analyzed. The approach is analogous to the one proposed over the past years for orthotropic materials by Piva andViola (1988) (Eng Fract Mech, 29: 535–548), and it may be considered an alternative to the mathematical formalisms currently used. A general expression of the stress field is determined in terms of complex potentials. The stress distribution and the displacement field in the proximity of the crack tip are finally obtained. An expression of the energy release rate is provided in terms of the field intensity factors. Numerical results are presented and discussed under different remote electro-mechanical loading conditions and varying the crack inclination. Particular attention has been focused on the effect of the lateral load on the fracture quantities and on the direction of the incipient branching angle.     

On a crack problem in an infinite circular cylinder with a penny-shaped crack under a transient thermal loading

In this paper we deal with finding the stress intensity factors under the transient thermal loading in a circular cylinder with infinite length containing a penny-shaped crack. Variations of the stress intensity factors with time, which are closely related with the crack propagations, are obtained and illustrated in figures. From these figures we can obtain useful suggestions respecting crack propagation.

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Résumé On traite, dans cette étude, de la recherche des facteurs d'intensité de contraintes dans un cylindre circulaire de longueur infinie comportant une fissure en forme d'angle et soumise à sollicitation thermique en régime transitoire.On obtient, et on donne des valeurs à titre d'exemples pour les variations de facteur d'intensité des contraintes en fonction du temps, qui sont en relation étroite avec la propagation de la fissure. Ces valeurs conduisent à des suggestions utiles en ce qui regarde la propagation d'une fissure.

     

A crack tip field estimation technique for the high-temperature cyclic loading of structures

The purpose of this paper is to present a methodology for the assessment of the near‐crack tip fields in structures operating at elevated temperatures in the creep range and subjected to cyclic mechanical and thermal loads. The method involves generating simplified extreme solutions, which corresponds to very short (rapid cycle) and long (slow cycle) cycle times, bounding the behaviour for intermediate cycle times. In such situations, by examining the increments of strain over a cycle of loading at the crack tip, the solutions may be related to the HRR fields and, hence, related to an equivalent constant load. Here, these solutions are generated using a nonlinear programming method, the linear matching method (LMM), on two bounding constitutive relationships with identical uniaxial data, Norton's law and the Bailey–Orowan model. These solutions are generated for the classical cracked axisymmetric Bree problem, presented as a contour of an equivalent path‐independent integral in creep, C*, by using a sampling point within an identified best‐matched HRR field.     

Creep crack growth under history-dependent loading

We discuss the influence of loading history on creep crack growth. Our attention is mainly focused on the following three aspects of this problem: (i) principal laws of history-dependent creep strain of materials; (ii) creep behavior of cracks, including the choice of suitable fracture parameters that may help to predict cracking; (iii) the importance of taking the history-dependent response of the material into account. We performed numerical calculations based on the use of an appropriate constitutive model and fracture theory for (1) and (2), respectively, to analyze results of tests for (3).Battelle, Columbus, Ohio. UES Incorporated, Dayton, Ohio. Published in Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 30, No. 4, pp. 37–45, July – Augus, 1994.