The near tip stress and strain fields in cracked single crystals

The numerical analyses of stationary mathematically sharp Mode I crack in FCC and BCC crystals with elastic-ideally plastic (EIP) and fast hardening saturation (FHS) law are carried out in the present paper. From the calculated results, it is shown that: for the cases of small strain, EIP crystal cracks, the features of concentrated deformation patterns and the stress state in near-crack tip deformation fields are identical to the earlier analytical solutions, but along the angular sector boundaries, there exist narrow complex stress zones. The overall characteristics of deformation patterns for the cases of EIP and FHS are similar. The behaviours of crack tip opening can be characterized by crack-tip-opening-displacement (CTOD). For the case of FHS, finite deformation BCC crystal crack, our calculations are qualitatively in agreement with recent experimental observations. The project supported by National Natural Science Foundation of China     

On the asymptotics of the stress and strain fields near a crack tip

The problem is solved under the plane strain conditions for a crack of general form, which in general is neither a mode I nor a mode II crack. We assume that the strains are small and the material is nonlinearly elastic. The mathematical statement of the problem is reduced to the eigenvalue problem for a system of ordinary nonlinear differential equations. Its solution is obtained numerically. We show that, for an incompressible material with power-law relations between the stress and strain deviators, the solution (the well-known HRR-asymptotics [1, 2]) exists only for mode I and II cracks. In the general case, we can only speak of approximate solutions. A similar conclusion can be made for different-modulus materials. We analyze the results of the preceding papers [1–7], where specific cases of the problem were considered.     

Measurement of the strain field near a crack tip in polymethylmethacrylate by holographic interferometry

An experimental method has been developed for the detailed, real-time study of the strain field near a crack tip in any transparent material. This method combines holography and interferometry to measure the field of averaged transverse strain in a sheet specimen under inplane loading. It is shown that the solution for an edge crack in a semi-infinite sheet based on two-dimensional linear elastic theory can be applied to the finite-width polymethylmethacrylate specimen. This solution is observed to become less valid as the crack tip is approached due to the breakdown of the plane-stress assumption. This effect is evaluated for a range of thicknesses from much less to much more than the crack length.     

Stress-concentration factors for elliptical holes near an edge

Experimental and theoretical stress-concentration factor and stress-intensity factor solutions exist for a large number of hole shapes and configurations. However, little work has been done on the interaction between holes and free edges. This paper reports the results of an experimental study which investigated elliptical holes close to each edge of a tension plate. The holes were symmetric with respect to the longitudinal axis of the models and had their major axes normal to the edge of the plate. The ellipse ratio and the distance between the center and the edge were varied. A statistical model is developed which shows that the stress concentrationK _g at both ends of the ellipses is linearly dependent on a geometric function ? such thatK _g = αΦ + γ. The values for the function ? are given.     

Measurement of inhomogeneous strain fields by fiber optic sensors embedded in a polymer composite material

Experimental results of strain field measurement in polymer composite specimens by Bragg grating fiber optic strain sensors embedded in the material are considered. A rectangular plate and a rectangular plate with “butterfly” shaped cuts are used as specimens. The results of uniaxial strain experiments with rectangular plates show that fiber optic strain sensors can be used to measure the strains, and these results can be used to calculate the calibration coefficients for fiber optic strain sensors. A gradient strain field is attained in a plate with cuts, and the possibility of measuring this field by fiber optic strain sensors is the main goal of this paper. The results of measurements of gradient strain fields in the plate with cuts are compared with the results obtained by using the three-dimensional digital optic system Vix-3D and with the results of numerical computations based on finite element methods. It is shown that the difference between the strain values obtained by these three methods does not exceed 5%.     

Atomistic and continuum studies of stress and strain fields near a rapidly propagating crack in a harmonic lattice

Large-scale atomistic simulations of a mode I crack propagating in a harmonic lattice are presented. The objective of this work is to study the stress and strain fields near a rapidly propagating mode I crack. The asymptotic continuum mechanics solutions of the elastic fields are compared quantitatively with molecular-dynamics simulation results for different crack velocities. It is observed that both atomistic stress and atomistic strain can be successfully related to the corresponding continuum quantities. The study reveals that the atomistic simulation results agree well with the continuum theory predictions, which suggests that the continuum theory can be applied for nano-scale dynamic problems.     

有限厚双边U型切口板的三维弹塑性有限元分析

针对单向拉伸载荷作用下的有限厚双边 U型切口板 ,本文对其切口根部的三维效应进行了详细的三维弹塑性大变形有限元分析 ,得到了不同于平面切口问题的新结果 :( 1 )在线弹性阶段 ,三维切口根部的应力集中因子 Kt高于二维情形 ,且 Kt在板厚 ( B)约为 8倍切口根部半径 (ρ)时达到峰值 ;进入塑性后 ,切口根部的 Kt随载荷水平的增加逐渐下降 ,并介于平面应力和平面应变情形之间 ;( 2 )切口前缘等效应变εe的最大值出现在约束最高的中面 ,且可比约束最低的自由表面处的应变值高一倍 ;( 3)薄板中 ,塑性区尺寸 xp 的最大值不是出现在约束较低的自由表面 ,而是出现在约束较高的中面 ,但随 B/ρ的增大逐渐向自由表面外推 ;( 4 )面内应力比 Tx在切口根部塑性区内的分布对板厚和载荷水平不敏感 ,可以用 Hill的滑移线解很好地近似。另外 ,对三维影响区内一些重要的三维约束参量进行了详细分析 ,总结了它们的三维分布规律。     

Low-cycle fatigue-crack indications by strain gages operating in elastic strain fields

This paper describes the response of bonded electrical-resistance strain gages to low-cycle fatigue cracking of four, cyclically pressurized, boxlike structures. The strain-pressure “signatures” of gages installed on flexural parts of the structures were recorded semicontinuously. By observing the changes in signatures of certain gages, it was possible to follow indirectly the initiation and propagation of internal low-cycle fatigue cracks. The described technique appears feasible as a crack-detection system, or as an adjunct to some other type of damage-warning system. It is suggested that the sensitivity and accuracy of this technique make it possible to substitute “crack initiation” for “through cracking” as a criterion for fatigue failure in design.     

On discontinuous strain fields in finite elastostatics

A general method for the study of piece-wise homogeneous strain fields in finite elasticity is proposed. Critical homogeneous deformations, supporting strain jumping, are defined for any anisotropic elastic material under constant Piola–Kirchhoff stress field in three-dimensional elasticity. Since Maxwell’s sets appear in the neighborhood of singularities higher than the fold, the existence of a cusp singularity is a sufficient condition for the emergence of piece-wise constant strain fields. General formulae are derived for the study of any problem without restrictions or fictitious stress–strain laws. The theory is implemented in a simple shearing plane strain problem. Nevertheless, the procedure is valid for any anisotropic material and three-dimensional problems.     

Thermal stress state near edge cracks in a plane with elliptical holes

S. P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kiev. Poltava Agricultural Institute, Poltava. Translated from Prikladnaya Mekhanika, Vol. 31, No. 11, pp. 90–96, November, 1995.     

Measurement of velocity fields in ball mills

This paper describes a computer vision technique used in measuring the velocity field related to the motion of balls in a ball mill. A camera combined with two color flashes facing an experimental ball mill is used to take pairs of pictures by triggering the flashes in sequence with a time interval Δt. In order to ensure consistency, the pictures are of different colors and in a single frame. The ball positions in each image are detected by image-processing techniques, and the velocity is then the displacement of each ball between two successive images divided by Δt. The measurement error is estimated by measuring the displacements from a pair of images when the balls remain stationary.     

Large strain field near a notch-tip under tension

This paper considers the plane strain notch-tip filed in a rubber-like material under tension. Based on a new constitutive relation, the asymptotic equations of the near tip field are derived and solved. It is shown that the notch tip field is composed of two narrowing sectors and an expanding sector. The dominant stress and strain near the notch tip are found to be in a state of uniaxial tension.     

Measurement of the temperature field downstream of simulated leading-edge film-cooling holes

Experiments to measure the temperature field downstream of simulated leading-edge-region film-cooling holes were performed in an 11 m/s wind tunnel flow. Heated air was passed to a hollow 140 mm diameter cylinder in which three 10.5 mm diameter, spanwise-inclined, film-cooling holes had been machined. A fine nylon mesh, coated with encapsulated thermochromic liquid crystals, was used to measure temperature contours downstream of the holes by moving the mesh relative to the holes and adjusting the power to the air heater. The measurements indicate the extent of the lateral spreading of the coolant gas and show the influence of hole location and coolant mass flow rate on film trajectory and spreading. Received: 5 February 1998/ Accepted: 22 October 1998     

V型缺口裂端的三维应力状态及约束分析

利用三维有限元方法,研究了有限厚度板中V型缺口根部穿透裂纹前沿的三维弹性应力场。对不同厚度、不同缺口张开角和裂纹长度对应力强度因子及裂尖附近的三维约束程度的影响进行了分析,同时还讨论了三维约束区的大小。研究结果显示：当缺口张开角小于60度时,不同缺口的应力强度因子和离面约束因子的分布基本一致,角度的影响不明显。应力强度因子是厚度的函数,板中面的应力强度因子随厚度的增加逐渐减小趋近干平面值,最大为1．08倍的平面值。当板厚超过15倍的缺口深度时,应力强度因子最大值将从中面转移至接近自由表面位置,距中面约0．4倍板厚。三维约束非常明显的区域在裂尖前沿约0.45倍厚度的范围内．二维到三维的过渡区在裂尖前沿1.5倍厚度的区域内;在中面上三维效应影响区最大,随着离中面距离的增加逐渐减小,在自由表面上降为0。     

Stress wave fields in plates weakened by curvilinear holes with edge cracks

The dynamic fracture of plates weakened by holes with edge cracks and subjected to impulsive loading is studied using the dynamic photoelastic method. The time dependences of the stress intensity factors and the crack growth rate are examined for three models of plates with circular holes and edge cracks __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 79–84, February 2006.     

On the synthesis of acoustic sources with controllable near fields

In this paper we present a strategy for the synthesis of acoustic sources with controllable near fields in free space and constant depth homogeneous ocean environments. We first present the theoretical results at the basis of our discussion and then, to illustrate our findings we focus on the following three particular examples:

• 1.acoustic source approximating a prescribed field pattern in a given bounded sub-region of its near field.
• 2.acoustic source approximating different prescribed field patterns in given disjoint bounded near field sub-regions.
• 3.acoustic source approximating a prescribed back-propagating field in a given bounded near field sub-region while maintaining a very low far field signature.

For each of these three examples, we discuss the optimization scheme used to approximate their solutions and support our claims through relevant numerical simulations.