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Full-Field Strain Measurement Integrated with Two Dimension Regression Analysis to Evaluate the Bi-Modulus Elastic Properties of Isotropic and Transversely Isotropic Materials

Journal Article · · Experimental Mechanics
 [1];  [2];  [2]
  1. Oklahoma State Univ., Tulsa, OK (United States); University of Al-Qadisiyah, Al-Diwaniyah (Iran); Oklahoma State University
  2. Oklahoma State Univ., Tulsa, OK (United States)

Background: Measuring the physical properties of shale is critical for optimizing engineering activities such as geothermal energy generation and hydraulic fracturing. Shale is a transversely isotropic material. Furthermore, this material can also include micro and macro cracks at different locations and orientations that cause it to behave differently under tensile or compressive loading. Objective: In this work, a combined experimental–numerical approach is proposed to evaluate the bi-modulus elastic properties of isotropic and transversely isotropic materials. Methods: Full-field strain measurements for a circular disk under diametral compression are integrated with a regression analysis technique to evaluate the elastic properties of bi-modulus materials subjected to tensile and compressive loads using two loading configurations on the same specimen. Digital Image Correlation (DIC) is used to measure the full-field strains. Subsequently, in the case of an isotropic material, a linear least-squares approach is utilized to process the experimentally determined strains in conjunction with analytical expressions of the stress fields (in terms of far-field loading) to determine the elastic modulus E, the shear modulus G, and the Poisson’s ratio $$v$$. In the case of a transversely isotopic material, such as shale, a finite element model is implemented to determine the stress fields (again in terms of far-field loading), which is followed by repeating the previous regression analysis in an iterative process to estimate the elastic parameters. Results: The results show that the proposed technique successfully provides a complete set of elastic properties as a function of both the loading condition and the principal material directions. The technique is validated by measurements on a known isotropic material and then applied to determine the properties of shale. Conclusion: In this work, the proposed approach is successfully used to calculate the bi-modulus elastic response of poly(methyl meth- acrylate) (PMMA) and shale. As expected, PMMA exhibits an isotropic response with no bi-modulus effect, however, shale exhibits both transverse isotropy and a bi-modulus effect. Therefore, this approach holds promise for investigating the elastic properties of materials like rocks and fiber-reinforced composite laminates as functions of the principal material directions and the loading conditions.

Research Organization:
Oklahoma State Univ., Stillwater, OK (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
FE0031777
OSTI ID:
2346208
Journal Information:
Experimental Mechanics, Journal Name: Experimental Mechanics Journal Issue: 1 Vol. 64; ISSN 0014-4851
Publisher:
SpringerCopyright Statement
Country of Publication:
United States
Language:
English

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