The Relationships between Weight Functions, Geometric Functions,and Compliance Functions in Linear Elastic Fracture Mechanics

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Linear elastic fracture mechanics is widely used in industry because it established simple and explicit relationships between the permissible loading conditions and the critical crack size that is allowed in a structure. Stress intensity factors are the above-mentioned functional expressions that relate load with crack size through geometric functions or weight functions. Compliance functions are to determine the crack/flaw size in a structure when optical inspection is inconvenient. As a result, geometric functions, weight functions and compliance functions have been intensively studied to determine the stress intensity factor expressions for different geometries. However, the relations between these functions have received ... continued below

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Yuan, Rong February 6, 2007.

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Linear elastic fracture mechanics is widely used in industry because it established simple and explicit relationships between the permissible loading conditions and the critical crack size that is allowed in a structure. Stress intensity factors are the above-mentioned functional expressions that relate load with crack size through geometric functions or weight functions. Compliance functions are to determine the crack/flaw size in a structure when optical inspection is inconvenient. As a result, geometric functions, weight functions and compliance functions have been intensively studied to determine the stress intensity factor expressions for different geometries. However, the relations between these functions have received less attention. This work is therefore to investigate the intrinsic relationships between these functions. Theoretical derivation was carried out and the results were verified on single-edge cracked plate under tension and bending. It is found out that the geometric function is essentially the non-dimensional weight function at the loading point. The compliance function is composed of two parts: a varying part due to crack extension and a constant part from the intact structure if no crack exists. The derivative of the compliance function at any location is the product of the geometric function and the weight function at the evaluation point. Inversely, the compliance function can be acquired by the integration of the product of the geometric function and the weight function with respect to the crack size. The integral constant is just the unchanging compliance from the intact structure. Consequently, a special application of the relations is to obtain the compliance functions along a crack once the geometric function and weight functions are known. Any of the three special functions can be derived once the other two functions are known. These relations may greatly simplify the numerical process in obtaining either geometric functions, weight functions or compliance functions for new test geometries.

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  • Report No.: LBNL--62486
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 901678
  • Archival Resource Key: ark:/67531/metadc880091

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  • February 6, 2007

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  • Sept. 22, 2016, 2:13 a.m.

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  • Sept. 30, 2016, 2:37 p.m.

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Yuan, Rong. The Relationships between Weight Functions, Geometric Functions,and Compliance Functions in Linear Elastic Fracture Mechanics, thesis or dissertation, February 6, 2007; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc880091/: accessed August 16, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.