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.     

Conditions for laminated plates to remain flat under inplane loading

There is considerable confusion in the existing literature as to whether an unsymmetrically laminated, composite plate will remain flat due to the application of inplane compressive or shear loads. If it does not remain flat, then bifurcation buckling would not normally take place, and transverse displacements would occur no matter how small the inplane loads. This paper investigates the conditions under which arbitrarily laminated and arbitrarily loaded plates remain flat, and therefore when buckling can occur. It is demonstrated that for uniform or linearly varying inplane loads no transverse pressure is necessary to keep a plate flat, although edge moments or transverse forces may be required at the boundaries.     

Failure assessment of notched polycrystalline graphite under tensile-shear loading

The fracture load and the fracture initiation angle were experimentally measured for a V-notched specimen made of polycrystalline graphite under combined tensile-shear loading. The experimental results were obtained for several specimens with different notch angles and various notch tip radii. The experimental observations showed that for a constant notch tip radius, the fracture load in pure tensile loading conditions decreases as the notch angle increases. Moreover, for a constant notch angle, as the notch tip radius increases the fracture load in graphite specimens enhances in the entire domain between pure tensile and pure shear loading conditions. A recently developed failure criterion was then used to estimate the experimental values of the notch fracture resistance and the fracture initiation angle for the tested graphite specimens. The experimental results could be estimated very well by using the results of the proposed criterion.     

Experimental investigation of fracture damage of notched granite beams under cyclic loading using DIC and AE techniques

Fracture experiments of three‐point bending notched granite beams were performed under cyclic loading using digital image correlation (DIC) and acoustic emission (AE) techniques. The damage evolution process of the specimen under cyclic loading was analysed on the basis of AE ring count and b value. The strain and displacement fields and the fracture process zone (FPZ) ahead of the crack tip were revealed by DIC. The results showed that the AE characteristics of rock fracture indicated a noticeable Kaiser effect in the stage of cyclic loading and unloading. Moreover, when the loading force reached 70% of its peak value, the AE characteristics showed the Felicity effect. The damage produced during the loading‐unloading process contributed to the development of the cracks leading to the catastrophic fracture. Besides, a relatively high loading rate was found to help to suppress the development of the FPZ at the crack tip.     

Effects of repeated loading on the fracture behavior of notched TiAl specimens

Notched specimens of a fully lamellar TiAl alloy and a duplex TiAl alloy were in situ tensile tested with repeated loading-unloading-reloading processes in a scanning electron microscope (SEM). The step-by-step processes of initiation and extension of the main crack were captured by SEM. The fracture surfaces were observed and one-sector-to-one-sector related to the crack extension. Effects of loading-unloading damage on the fracture behavior were evaluated by combining the pictures of propagating crack configurations, corresponding fracture surfaces and the load locus. The results revealed the following events: (1) at the elastic regime, the loading-unloading process had negligible effect on the fracture behavior produced by subsequent reloading; (2) at the plastic regime, even at a value much lower than that of the preload, the reload extended further the existing main crack; (3) after a heavy loading-unloading process, the main crack extended and resulted in final fracture at a value of the reload, which was lower than that of the preload and (4) microcracks produced in the loading-unloading process had minor effects on the fracture behavior.     

Failure mechanisms of a notched CFRP laminate under multi-axial loading

A quasi-isotropic CFRP laminate, containing a notch or circular hole, is subjected to combined tension and shear, or compression. The measured failure strengths of the specimens are used to construct failure envelopes in stress space. Three competing failure mechanisms are observed, and for each mechanism splitting within the critical ply reduces the stress concentration from the hole or notch: (i) a tension-dominated mode, with laminate failure dictated by tensile failure of the 0° plies, (ii) a shear-dominated mode entailing microbuckling of the −45° plies, and (iii) microbuckling of the 0° plies under remote compression. The net section strength (for all stress states investigated) is greater for specimens with a notch than a circular hole, and this is associated with greater split development in the load-bearing plies. The paper contributes to the literature by reporting sub-critical damage modes and failure envelopes under multi-axial loading for two types of stress raiser.     

Quantification of constraint effects in fracture mechanism transition for cracked structures under mixed mode loading

The objective of the study is to evaluate the effects of plastic constraint on transition between tensile-type and shear-type fracture. The T -stress is employed as the quantifying parameter for constraint and is incorporated into the existing theoretical criteria for modelling this transition. It is found that different constraint levels can dramatically alter the transition point. To verify this finding, two sets of mixed mode tests with different constraint levels are carried out. Alongside the theoretical and experimental study, finite element simulation is performed to verify and support these findings. Substantially improved agreement is observed with experimental data if the effect of plastic constraint on transition is included.     

Prediction methods of fatigue critical point for notched components under multiaxial fatigue loading

Two methods based on local stress responses are proposed to locate fatigue critical point of metallic notched components under non‐proportional loading. The points on the notch edge maintain a state of uniaxial stress even when the far‐field fatigue loading is multiaxial. The point bearing the maximum stress amplitude is recognized as fatigue critical point under the condition of non‐mean stress; otherwise, the Goodman's empirical formula is adopted to amend mean stress effect prior to the determination of fatigue critical point. Furthermore, the uniaxial stress state can be treated as a special multiaxial stress state. The Susmel's fatigue damage parameter is employed to evaluate the fatigue damage of these points on the notch edge. Multiaxial fatigue tests on thin‐walled round tube notched specimens made of GH4169 nickel‐base alloy and 2297 aluminium‐lithium alloy are carried out to verify the two methods. The prediction results show that both the stress amplitude method and the Susmel's parameter method can accurately locate the fatigue critical point of metallic notched components under multiaxial fatigue loading.     

组合载荷下含缺口纤维增强树脂基复合材料的失效分析

为研究含缺口纤维增强复合材料层合板在复杂载荷下的破坏,本文采用改进的Arcan夹具,在30°方向对含缺口碳纤维增强树脂基复合材料层合板（[-45/90/45/0]_s）进行了拉伸-剪切组合加载实验。用数字图像相关方法（DICM）测量了层合板表面层的裂纹发展过程,在缺口尖端观察到了明显的劈裂现象。然后用有限元软件ABAQUS建立了三维层合板模型,为准确模拟裂纹尖端的应力场,模型中每层引入内聚力接触来模拟劈裂。为了比较加载端的转动自由度对层合板失效模式和破坏强度的影响,文中分析了两种不同的边界条件,即约束和放松加载端的转动自由度。研究结果发现,加载端的合力方向主导了层合板的失效模式和破坏强度,放松加载端自由度的模拟结果与实验结果有很好的一致性。     

Torsional oscillation of tapered rods under arbitrary lateral loading

We consider steady-state torsional oscillation of a tapered rod under the action of tangential forces, which are arbitrarily distributed over its lateral surface, and twisting moments applied to its ends. To solve this problem, we suggest a method based on the series expansion of the displacement function in a nondimensional parameter which depends on the characteristics of the material and the frequency of loading. We present computational investigations for particular cases of loading. Translated from Problemy Prochnosti, No. 3, pp. 62–68, May–June, 1998.     

Short-crack-growth-based fatigue assessment of notched components under multiaxial variable amplitude loading

A short crack model originally proposed for multiaxial constant amplitude loading is extended and applied to multiaxial variable amplitude loading. Load sequences have a significant influence on variable amplitude life; they are taken into account using algorithms originally proposed only for uniaxial loading. The estimated fatigue lives of unnotched tubular specimens and notched shafts under different in- and out-of-phase multiaxial constant and variable amplitude load histories are compared with the experimental results. The comparison reveals that the proposed short crack approach enables sufficiently accurate estimation. Moreover, the estimated critical planes, i.e., the planes of maximum crack growth rate or minimum life, are in good agreement with the experimental observations.     

Dynamic fracture under plane wave loading

A new plate impact experiment is presented for studying dynamic fracture processes that occur under sub-microsecond loading. The experiment is designed to provide comparatively straightforward interpretation within the framework of fracture mechanics. A disc containing a mid-plane, pre-fatigued, edge crack that has been propagated halfway across the diameter is impacted by a thin flyer plate of the same material. A compressive pulse propagates through the specimen and reflects from the rear surface as a step, tensile pulse with a duration of 1s. This plane wave loads the crack and causes initiation and propagation of the crack. The motion of the rear surface is monitored during this event using a laser interferometer system. The location of the crack front is mapped before and after the experiment using a focussed ultrasonic transducer.Experiments have been conducted on a hardened 4340 VAR steel at temperatures ranging from room temperature to — 100°C. Crack advance increases monotonically with increasing impact velocity and with decreasing temperature. Critical values of the stress intensity factorK _Ic are inferred from known elastodynamic solutions and the assumption that the measured crack advance occurs at a constant energy release rate. Fracture modes are characterized by means of scanning electron microscopy of the fracture surfaces.A finite difference method is used for numerical simulation of the experiments. The loading is modelled as that of a plane, square, tensile pulse impinging at normal incidence on a semi-infinite crack. Crack advance is assumed to initiate when the crack-tip stress intensity factor reaches the critical valueK _Ic. Crack velocities are prescribed corresponding to various fracture models. The predicted motion of the rear surface is found to be in good agreement with the measured motion when the crack velocity is taken to be a constant.

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Résumé On présente un nouvel essai de choc sur plaque pour l'étude du processus de rupture dynamique qui se produit sous des charges inférieures à la micro-seconde. L'essai est conçu de manière à fournir une interprétation comparativement directe dans le cas de las mécanique de la rupture. L'essai consiste à soumettre à un choc un disque comportant une fissure du bord suivi un plan médian, préfatiguée et propagée sur la moitié du diamètre du disque, à l'aide d'une plaque mince mobile du même matériau. Une impulsion de compression se propage au travers de l'echantillon, se réfléchit sur la surface arrière comme sur un seuil, entraînant une impulsion de traction avec une durée d'une micro-seconde. Cette onde plane soumet la fissure à la sollicitation et provoque l'amorçage de la propagation de la fissure. On enregistre le mouvement de la surface arrière au cours du phénomène en utilisant un système d'interférométrie à laser. La localisation du front de fissure est tracée avant et après l'essai, en utilisant un transducteur ultrasonique focalisé.Des essais ont été conduits sur un acier 4340 Var durci, à des températures comprises entre la température ambiante et — 100°C. L'avancement de la fissure augmente de manière monotone avec les vitesses croissantes de choc et avec l'abaissement de la température. Des valeurs critiques des facteurs d'intensité de contrainteK _lc, sont déduites à partir des solutions élasto-dynamiques connues et de l'hypothése que l'avancement de la fissure mesurée se produit suivant une vitesse de relaxation en énergie constante. Les modes de rupture sont caractérisés au moyen de la microscopie électronique à balayage des surfaces de rupture.Une méthode finie différentielle est utilisée pour l'assimiliation numérique des essais. La mise en charge est modélisée comme celle d'une impulsion de traction plane et carrée agissant suivant une incidence normale sur une fissure semi-infinie. L'avancement de la fissure est supposé commencer lorsque le facteur d'intensité de contrainte à son extrémité atteint la valeur critiqueK _Ic. Les vitesses de fissuration sont établies en correspondance avec différents modèles de rupture. On trouve que le mouvement prévu de la surface arrière est en bon accord avec les mouvements mesurés, lorsque la vitesse de fissuration est considérée comme constante.

     

A thermal imaging technique for studying crack development in wood under torsional loading

A thermal imaging system has been used for monitoring fracture in wood under both static and fatigue torsional loading. The thermal images of softwood test-pieces containing a knot under torsional loading predicted the cracking time and crack position that agreed well with visual observation. The thermal images obtained under torsional fatigue loading indicated a temperature increase during the unloading part of a loading cycle, which meant that thermal energy was dissipated during the relaxation stage of the loading cycle. The maximum temperature reached also increased as the loading cycles increased. Results from thermal images of a softwood indicated that the earlywood exchanged more thermal energy than latewood. Optical microscopy and SEM confirmed that in earlywood the region near a growth ring is the weaker area. For all the test pieces, whether softwood or hardwood, with or without a knot, the hotspots revealed during thermal imaging appeared before the load dropped sharply and these were confirmed to be the positions for crack initiation. This shows that it is possible to predict and depict failure and its progress using thermal imaging techniques.     

Crack propagation in notched specimens of porous silicon carbide under cyclic loading

Notched specimens of porous silicon carbide with porosity 37% were fatigued under four‐point bending at frequencies of 30 and 0.3 Hz. The fatigue life expressed in terms of time was rather insensitive to the test frequency, while that expressed in terms of cycles was much shorter for the case of 0.3 Hz than for 30 Hz. A time‐dependent mechanism of stress corrosion cracking was mainly responsible for crack propagation, and stress cycling enhanced the crack‐propagation mechanism. The crack length was estimated from the change in compliance of the specimen. The crack‐propagation curve was divided into stages I and II. In stage I, the crack‐propagation rate decreased even though the applied stress intensity factor became larger with crack extension, and then turned to increase in stage II. The transition from stage I to II took place at a crack extension of around 0.8 mm. This anomalous behaviour is caused by crack‐tip shielding due to microcracking and asperity contact. Fractographic observations showed that the fracture path was along the binder phase between silicon carbide particles, or more precisely along the interface between particles and binders.     

Weibull stress model for cleavage fracture under high-rate loading

This paper examines the effects of loading rate on the Weibull stress model for prediction of cleavage fracture in a low-strength, A515-70 pressure vessel steel. Interest focuses on low-to-moderate loading rates ( K˙ _I < 2500  MPa √m  s⁻¹ ). Shallow cracked SE(B) specimens were tested at four different loading rates for comparison with previous quasi-static tests on shallow notch SE(B)s and standard C(T)s. To utilize these dynamic experimental data, we assume that the Weibull modulus ( m ) previously calibrated using quasi-static data remains invariant over the loading rates of interest. The effects of dynamic loading on the Weibull stress model enter through the rate-sensitive material flow properties, the scale parameter ( σ _u ) and the threshold Weibull stress ( σ _w-min ). Rate-sensitive flow properties are modelled using a viscoplastic constitutive model with uniaxial, tension stress–plastic strain curves specified at varying plastic strain rates. The analyses examine dependencies of σ _w-min and σ _u on K˙ _I . Present results indicate that σ _w-min and σ _u are weak functions of loading rate K˙ _I for this pressure vessel steel. However, the predicted cumulative probability for cleavage exhibits a strong sensitivity to σ _u and, consequently, the dependency of σ _u on K˙ _I is sufficient to preclude use of the static σ _u value for high loading rates.     

Discrete approach to study fracture energy absorption under dynamic loading

Behavior and peculiarities of failure of frame structures under dynamic loading are studied on the basis of computer modeling. The advantages of the Movable Cellular Automata (MCA) method allow to study all stages of the fracture process from damages generation to the complete failure. A possibility of the effect of elastic energy accumulation in complex structures is shown.