Model for Analysis of Biaxial and Triaxial Stresses by X-ray Diffraction Assuming Orthotropic Materials Edson M. Santos 1;2 , Marcos T. D. Orlando 2 , Milton S. R. Milta ˜o 1 , Luis G. Martinez 3 , Alvaro S. Alves 1;4 , and Carlos A. Passos 2 1 Laborato ´rio de Fı ´sica de Materiais, Departamento de Fı ´sica, Universidade Estadual de Feira de Santana, Av. Transnordestina, s/n, Novo horizonte, Campus Universitrio, Feira de Santana-BA, 44036-900, Brazil 2 Universidade Federal do Espı ´rito Santo, Av. Fernando Ferrari, 514, Goiabeiras, Vito ´ ria-ES, 29060-910, Brazil 3 Instituto de Pesquisas Energe ´ ticas e Nucleares, Av. Lineu Prestes 2242, Cidade Universita ´ria, Sa ˜ o Paulo-SP, 05508-000, Brazil 4 Instituto de Fı ´sica, Universidade Federal Fluminense, Av. Gal. Milton Tavares de Souza, s/n, Campus da Praia Vermelha, Nitero ´ i-RJ, 24210-346, Brazil Received November 20, 2009; revised December 26, 2009; accepted January 4, 2010; published online May 20, 2010 In this work we aim to develop expressions for the calculation of biaxial and triaxial stresses in polycrystalline anisotropic materials, and to determine their elastic constants using the theory of elasticity for continuum isochoric deformations; thus, we also derive a model to determine residual stress. The constitutive relation between strain and stress in these models must be assumed to be orthotropic, obeying the generalized Hooke’s law. One technique that can be applied with our models is that of X-ray diffraction, because the experimental conditions are similar to the assumptions in the models, that is, it measures small deformations compared with the sample sizes and the magnitude of the tensions involved, and is insufficient to change the volume (isochoric deformation). Therefore, from the equations obtained, it is possible to use the sin 2 technique for materials with texture or anisotropy by first characterizing the texture through the pole figures to determine possible angles that can be used in the equation, and then determining the deformation for each diffraction peak with the angles obtained from the pole figures. # 2010 The Japan Society of Applied Physics DOI: 10.1143/JJAP.49.056601 1. Introduction In materials science, the study of residual stress is of interest for a wide range of technological applications, for instance, thermal barriers and corrosion resistance on metallic structures, 1) mechanical stress in superconductor magnets, 2) residual tension in thin films, 3) corrosion fatigue in alloys widely used for the structural components of older aircraft, 4) and so forth. Thus, the importance of developing models that enable the investigation of residual stress is clear. In this work we define the material stress as the internal stress existing in a material when it is not submitted to external forces. 5) Thus, we can classify the material stress as intrinsic and extrinsic. . Intrinsic stress appears during the process of material growth and generally originates from the defects incorporated in the material structure. . Extrinsic stress appears after the process of material growth and in general its causes are the thermal and mechanical effects on the materials. From the experimental point of view, the residual stress in materials can be determined by different methods and techniques: . Mechanical methods are linear and are based on applying dissection and section methods to the sample. Examples of dissection methods include the ring-core method and the hole-drilling method; an example of a section method is the material-removing method. 6) These mechanical methods are destructive. . Nonlinear elastic methods involve the inelastic mod- ification of the sample structure, examples include the ultrasonic and magnetic techniques. 7) . Diffraction techniques are linear and based on the diffraction phenomenon because of the wave incidence over the sample by elastic spreading. Examples include X-ray diffraction 1,3) and neutron diffraction. 8,9) These methods are not destructive. The stresses cannot be directly measured. To obtain the stress we need to measure various properties of the material such as the deformation. 1,8,10) The methods given above give the deformation. Stresses in a material originate from many sources, and in general they can be divided into three categories 11) accord- ing to their length scale. . Type I stress, which acts at a scale of a large number of grains (i.e., millimeters), is, by definition, independ- ent of individual grain orientation and is known as the macrostress. 11) It is homogeneous over very large crystal domains of the materials. 12) . Type II stress (intergranular stress), which varies from grain to grain, is homogeneous within a small number of crystal domains of the material (a single grain or phase). 12) . Type III stress, which originates from local defects and fluctuates within a grain, is homogeneous within the smallest crystal domains (over several atomic dis- tances). 12) In the case of real materials, the actual stress state at a point results from the superposition of stress types I, II, and III. The stress is strongly dependent on the material’s anisotropy. As is well known, a crystal is characterized as a periodic array of its elements in space. For this reason a dependence of the crystalline properties on the direction is generated, known as anisotropy. Most natural and artificial solids contain many crystallites, which can have different sizes, forms and orientations. The crystallites are units of the microscopic monocrystals of the material. The preferential orientation of the crystallites inside a material is called the texture. 13) The texture is an intrinsic characteristic of metals, ceramics, polymers, and rocks and it has a strong effect on the anisotropy of the physical properties of a material. E-mail address: [email protected] Japanese Journal of Applied Physics 49 (2010) 056601 REGULAR PAPER 056601-1 # 2010 The Japan Society of Applied Physics
Model for Analysis of Biaxial and Triaxial Stresses by X-ray Diffraction Assuming Orthotropic Materials
May 19, 2023
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Related Documents
