A technique for the complete nondestructive evaluation of plane states of residual stress is presented. This technique is based on the acoustoelastic effect in which the presence of the residual stress causes a shift in the speed at which a wave propagates through the material. The particular acoustoelastic technique considered here employs longitudinal waves propagating normal to the plane of the stress. Such waves experience a shift in propagation speed which, for an isotropic material, is proportional to the sum of the principal stresses. A Poisson’s equation for the in-plane shear stress is obtained from the two-dimensional equilibrium equations in which the forcing function is obtained directly from the measured velocity variations. Once this equation is integrated for the shear stress, the normal stresses may be evaluated directly from the equilibrium equations. In this paper, the basic equations are derived for the case of an anisotropic material. The experimental and numerical procedures are reviewed, and results of residual stresses in an aluminum ring are presented.

The acoustoelastic technique for the nondestructive evaluation of stress is based on the stress-induced changes in the speed of wave propagation. In the application of acoustoelasticity. three different approaches have been adopted. For the sake of discussion. we will consider the case of a plane state of stress in an initially isotropic material. The most common technique uses shear waves propagating normal to the plane of stress [1.2]. This technique takes advantage of the stress-induced birefringence of the shear waves which. in the case considered. is proportional to the difference in the principal stresses. Another technique which is currently receiving considerable attention involves two shear-horizontal (SH) waves propagating in the principal stress directions. with their polarizations in the other principal direction [3-5]. In this approach. the difference in the speeds of the two SH waves can be related to the difference in principal stresses directly. Knowledge of the material's elastic or acoustoelastic constants is not required. The final approach uses a single longitudinal wave propagating perpendicular to the plane of stress. with the change in the speed of this wave being proportional to the sum of the principal stresses [6.7].

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Finite element simulations using an internal state variable constitutive model coupled with a void growth and damage model are used to study weld solidification cracking of 6061-T6 aluminum. Calculated results are compared with data from an experimental program determining the locations of failure as a function of weld process parameters and specimen geometry. Two types of weld solidification cracking specimen were studied. One specimen, in which cracking did not occur, was used to evaluate finite element simulations of the thermal response and calculations of average strain across the weld. The other specimen type was used to determine the location of crack initiation as a function of weld process parameters. This information was used to evaluate the finite element simulations of weld solidification cracking. A solidification model which includes dendrite tip and eutectic undercooling was used in both thermal and mechanical finite element analyses. A strain rate and temperature history dependent constitutive model is coupled with a ductile void growth damage model in the mechanical analyses. Stresses near the weld pool are examined to explain results obtained in the finite element analyses and correlated with experimental observations. Good agreement is obtained between simulation and experiment for locations of crack initiation and extent of cracking. Some effects of uncertainties in material parameters are discussed. DISCLAIMERThis rrpon was F p a r d as an aQx)uat of work spowrrcd by an agency of the United States Gownmat Neither the Unitat Stam Government nor any agency &emf. nor any of their employes, mnkcr any #uranty, express or implied. or fuincss of m y information, apparatus, pmducr, or procar disciosai, or rrpraents that its w would not infringe privately owned igbu Rcfuencc herein to any rpafic c o m m d pmduct, proccu or wwice by trade rumt, tradmmk tnonufac-tu=. or otherwise docs not nccessoriiy QlLIttitlltc or impiy its atdorsrment. m mmend;ruon. or fawring by the United States Gonernmmt or any agency thereof. The views and Opinions of authors arprrued h d do not n d y state or rrfim those of the United States Government or any agency thereof. ==CS my legal linbility Or rrzp~art'bility for the -CY, C O m p i ~a l ~ OT W -DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

This report summarizes the efforts to develop and validate a finite element based model to predict weld solidification cracking behavior. Such a model must capture the solidification behavior, the thermal behavior in the weld pool region, the material mechanical response, and some failure criteria to determine when solidification cracking will occur. For such a program to be successful, each aspect of the model had to be accurately modeled and verified since the output of one portion of the model served as the input to other portions of the model. A solidification model which includes dendrite tip and eutectic undercooling was developed and used in both the thermal and mechanical finite element analysis. High magnification video techniques were developed to measure strains for validation of the mechanical predictions using a strain rate and temperature dependent constitutive model. This model was coupled with a ductile void growth damage model and correlated with experimental observations to determine capabilities of predicting cracking response. A two phase (solid + liquid) material model was also developed that can be used to more accurately capture the mechanics of weld solidification cracking. In general, reasonable agreement was obtained between simulation and experiment for location of crack initiation and extent of cracking for 606 1 -T6 aluminum.This page intentionally left blank 4