Experimental Analysis of Deformation Induced Microstructure Near a Crack Tip in a Hardened Copper Crystal

1998 ◽  
Vol 539 ◽  
Author(s):  
A.-F. Bastawros ◽  
K.-S. Kim

AbstractThe incremental in-plane Green-Lagrange strain tensor was measured near a stationary crack tip in a cyclically work-hardened copper single crystal. Measurements were made on the surface of a four-point bend specimen, using a finite-deformation laser moiré interferometer. The measurement showed the existence of a narrow asymptotic field beyond a distance of 300 μm from the crack tip. The inner boundary of the asymptotic zone was almost fixed at a characteristic distance ahead of the crack tip. This length scale is thought to arise from a microstructural evolution near the crack tip. The inhomogeneous hardening due to glide-band clustering and patchy slip in a small volume near the crack tip triggered such an evolution. The outer boundary of the asymptotic zone radially grew with the increasing load. The deformation field was found to be very sensitive to additional mode II loading.

2008 ◽  
Vol 08 (01) ◽  
pp. 131-159 ◽  
Author(s):  
RECEP GUNES ◽  
J. N. REDDY

Geometrically nonlinear analysis of functionally graded circular plates subjected to mechanical and thermal loads is carried out in this paper. The Green–Lagrange strain tensor in its entirety is used in the analysis. The locally effective material properties are evaluated using homogenization method which is based on the Mori–Tanaka scheme. In the case of thermally loaded plates, the temperature variation through the thickness is determined by solving a steady-state heat transfer (i.e. energy) equation. As an example, a functionally gradient material circular plate composed of zirconium and aluminum is used and results are presented in graphical form.


Author(s):  
K. Linga Murty ◽  
Chang-Sung Seok

Ferritic steels commonly used for pressure vessels and reactor supports in light water reactors (LWRs) exhibit dynamic strain aging (DSA) resulting in decreased ductility and toughness. In addition, recent work indicated decreased toughness during reverse-cyclic loading that has implications on reliability of these structures under seismic loading conditions. We summarize some of our recent work on these aspects along with synergistic effects, of interstitial impurity atoms (IIAs) and radiation induced point defects, that result in interesting beneficial effects of radiation exposure at appropriate temperature and strain-rate conditions. Radiation-defect interactions were investigated on pure iron, Si-killed mild steel, A533B, A516, A588 and other reactor support and vessel steels. In all cases, DSA is seen to result in decreased ductility accompanied by increased work-hardening parameter. In addition to mechanical property tests, fracture toughness is investigated on both A533B and A516 steels. While dips in fracture toughness are observed in A533B steel in the DSA region, A516 steel exhibited at best a plateau. The reasons could lie in the applied strain-rates; while J1c tests were performed on A533B steel using 3-point bend tests on Charpy type specimens, CT specimens were used for A516 steel. However, tensile and 3-point bend tests on similar grade A516 steel of different vintage did exhibit distinct drop in the energy to fracture. Load-displacement curves during J1c tests on CT specimens did show load drops in the DSA regime. The effect of load ratio (R) on J versus load-line displacement curves for A516 steel is investigated from +1 to −1 at a fixed normalized incremental plastic displacement of 0.1 (R = 1 corresponds to monotonic loading). We note that J-values are significantly reduced with decreasing load ratio. The work-hardening characteristics on the fracture surfaces were studied following monotonic and cyclic loading fracture tests along with the stress-field analyses. From the hardness and the ball-indentation tests, it was shown that decreased load ratio (R) leads to more strain hardening at the crack tip resulting in decreased fracture toughness. From the stress field analysis near the crack tip of a compact tension fracture toughness test specimen, a cycle of tensile and compressive loads is seen to result in tensile residual stresses (which did not exist at the crack tip before). These results are important to evaluations of flawed-structures under seismic loading conditions, i.e. Leak-Before-Break (LBB) and in-service flaw evaluation criteria where seismic loading is addressed. In addition, studies on fast vs total (thermal+fast) neutron spectra revealed unexpected results due to the influence of radiation exposure on source hardening component of the yield stress; grain-size of pure iron plays a significant role in these effects.


2013 ◽  
Vol 554-557 ◽  
pp. 919-927 ◽  
Author(s):  
Hamdaoui Mohamed ◽  
Guénhaël Le Quilliec ◽  
Piotr Breitkopf ◽  
Pierre Villon

The aim of this work is to present a POD (Proper Orthogonal Decomposition) based surrogate approach for sheet metal forming parametrized applications. The final displacement field for the stamped work-piece computed using a finite element approach is approximated using the method of snapshots for POD mode determination and kriging for POD coefficients interpolation. An error analysis, performed using a validation set, shows that the accuracy of the surrogate POD model is excellent for the representation of finite element displacement fields. A possible use of the surrogate to assess the quality of the stamped sheet is considered. The Green-Lagrange strain tensor is derived and forming limit diagrams are computed on the fly for any point of the design space. Furthermore, the minimization of a cost function based on the surrogate POD model is performed showing its potential for solving optimization problems.


1965 ◽  
Vol 32 (4) ◽  
pp. 826-828 ◽  
Author(s):  
Mark Levinson

Other investigators have extended the complementary energy theorem (Castigliano’s theorem) to cover the finite deformation of elastic systems with a finite number of degrees of freedom (structures) and they then have indicated that the extension of the theorem to cover the finite deformation of an elastic continuum involved certain unstated difficulties. The present paper shows that when the strain tensor and Trefftz stress tensor, the usual choice of conjugate deformation and stress tensors, are chosen to characterize the finite deformation of an elastic continuum, one cannot establish a strict complementary energy theorem. It is then shown that a strict complementary energy theorem for the finite deformation of an elastic continuum can be established if what Fritz John calls the Lagrange strain and Lagrange stress tensors are used as the conjugate deformation and stress tensors characterizing the deformation.


2002 ◽  
Vol 2002.2 (0) ◽  
pp. 59-60
Author(s):  
Mototsugu TANAKA ◽  
Akinori KONO ◽  
Masaki HOJO ◽  
Shojiro OCHIAI

Author(s):  
Blake Martin ◽  
Armaghan Salehian

Harnessing structural elements with strings, power cables, and signal cables increases the complexity in modelling the dynamic behaviour of such structures. Developing models capable of accurately predicting the dynamic behaviour of these systems is of great importance for space structures that cannot be tested prior to launch. The focus of this work is obtaining an equivalent continuum model for string-harnessed beam-like structures with periodic wrapping patterns. The tension in the string is assumed to vary as the beam deflects. The displacement field with second-order terms is determined and from which the Green-Lagrange strain tensor is obtained. After finding kinetic and potential energy expressions Hamilton’s principle is used to obtain the partial differential equation and boundary conditions. Numerical results for the shift in the natural frequencies are presented for various string properties to investigate their effects on the structure.


Materials ◽  
2019 ◽  
Vol 12 (19) ◽  
pp. 3200
Author(s):  
Sebastián Andrés Toro ◽  
Pedro Miguel Aranda ◽  
Claudio Moisés García-Herrera ◽  
Diego Javier Celentano

This work presents an experimental and numerical analysis of the mechanical behavior of a fixed-end SAE 1045 steel cylindrical specimen during the torsion test. To this end, an iterative numerical–experimental methodology is firstly proposed to assess the material response in the tensile test using a large strain elastoplasticity-based model solved in the context of the finite element method. Then, a 3D numerical simulation of the deformation process of the torsion test is tackled with this previously characterized model that proves to be able to predict the development of a high and localized triaxial stress and strain fields caused by the presence of high levels of angular deformation. Finally, the obtained numerical results are analytically studied with the cylindrical components of the Green–Lagrange strain tensor and experimentally validated with the measurements of shear strains via Digital Image Correlation (DIC) and the corresponding torque – twist angle curve.


2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Karthik Yerrapragada ◽  
Armaghan Salehian

This paper presents a distributed parameter model to study the effects of the harnessing cables on the dynamics of a host structure motivated by space structures applications. The structure is modeled using both Euler–Bernoulli and Timoshenko beam theories (TBT). The presented model studies the effects of coupling between various coordinates of vibrations due to the addition of the cable. The effects of the cable's offset position, pretension, and radius are studied on the natural frequencies of the system. Strain and kinetic energy expressions using linear displacement field assumptions and Green–Lagrange strain tensor are developed. The governing coupled partial differential equations for the cable-harnessed beam that includes the effects of the cable pretension are found using Hamilton's principle. The natural frequencies from the coupled Euler, Bernoulli, Timoshenko and decoupled analytical models are found and compared to the results of the finite element analysis (FEA).


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