Granite strength and toughness from small notched three-point-bend specimens of geometry dissimilarity

Xiangyu Han, Yi Chen, Xiaozhi Hu, Wen Liu, Qingbin Li, Shougen Chen

Research output: Contribution to journalArticle

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Abstract

Maximum fracture loads (Pmax)of small notched granite specimens under three-point-bending (3-p-b)conditions can be easily measured with any notch/size ratio. In this study, we report a simple closed-form solution of a non-Linear Elastic Fracture Mechanics (non-LEFM)model emphasizing the influence of average grain size G on quasi-brittle fracture of granite. This simple analytical solution containing the grain size G can be conveniently used to determine granite tensile strength ft and fracture toughness KIC from Pmax measurements of small notched 3-p-b specimens of geometry dissimilarity. The span/width (S/W)ratios of small 3-p-b specimens can vary, e.g. 2.5 or 4. The notch/width (a0/W)can also vary, e.g. the notch a0 can be as short as the average grain size (G), or close to width W. However, specimens with α-ratio (=a0/W)around 0.2 are recommended to minimize the boundary influence/effect from both the front and back specimen boundaries as proven by the Boundary Effect Model (BEM). Blue granite with the average grain size around 2 (mm)was selected to test the new method. Total 64 granite samples from four different groups (different 3-p-b sample designs)were tested, with W = 27, 40 and 70 (mm), S/W = 2.5, 4.0 and a0 = 4, 6 and 8 (mm). The tensile strength ft and fracture toughness KIC estimated from every group is fairly close to the values determined from the entire population of 64 tests. Therefore, tests from any specimen group of given geometry and size are sufficient. Estimations for G = 1.5 and 2.5 (mm)were also provided and compared with those for G = 2 (mm)to show the grain size influence. Advantages and disadvantages of BEM and well-known SEL (size effect law)are also discussed using the granite results.

Original languageEnglish
Article number106482
JournalEngineering Fracture Mechanics
DOIs
Publication statusE-pub ahead of print - 14 May 2019

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Granite
Toughness
Geometry
Fracture toughness
Tensile strength
Brittle fracture
Fracture mechanics
granite

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title = "Granite strength and toughness from small notched three-point-bend specimens of geometry dissimilarity",
abstract = "Maximum fracture loads (Pmax)of small notched granite specimens under three-point-bending (3-p-b)conditions can be easily measured with any notch/size ratio. In this study, we report a simple closed-form solution of a non-Linear Elastic Fracture Mechanics (non-LEFM)model emphasizing the influence of average grain size G on quasi-brittle fracture of granite. This simple analytical solution containing the grain size G can be conveniently used to determine granite tensile strength ft and fracture toughness KIC from Pmax measurements of small notched 3-p-b specimens of geometry dissimilarity. The span/width (S/W)ratios of small 3-p-b specimens can vary, e.g. 2.5 or 4. The notch/width (a0/W)can also vary, e.g. the notch a0 can be as short as the average grain size (G), or close to width W. However, specimens with α-ratio (=a0/W)around 0.2 are recommended to minimize the boundary influence/effect from both the front and back specimen boundaries as proven by the Boundary Effect Model (BEM). Blue granite with the average grain size around 2 (mm)was selected to test the new method. Total 64 granite samples from four different groups (different 3-p-b sample designs)were tested, with W = 27, 40 and 70 (mm), S/W = 2.5, 4.0 and a0 = 4, 6 and 8 (mm). The tensile strength ft and fracture toughness KIC estimated from every group is fairly close to the values determined from the entire population of 64 tests. Therefore, tests from any specimen group of given geometry and size are sufficient. Estimations for G = 1.5 and 2.5 (mm)were also provided and compared with those for G = 2 (mm)to show the grain size influence. Advantages and disadvantages of BEM and well-known SEL (size effect law)are also discussed using the granite results.",
keywords = "Average grain size (G), Boundary Effect Model (BEM), Fracture toughness, Granite, Size Effect Law (SEL), Statistical Scatter, Tensile strength",
author = "Xiangyu Han and Yi Chen and Xiaozhi Hu and Wen Liu and Qingbin Li and Shougen Chen",
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Granite strength and toughness from small notched three-point-bend specimens of geometry dissimilarity. / Han, Xiangyu; Chen, Yi; Hu, Xiaozhi; Liu, Wen; Li, Qingbin; Chen, Shougen.

In: Engineering Fracture Mechanics, 14.05.2019.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Granite strength and toughness from small notched three-point-bend specimens of geometry dissimilarity

AU - Han, Xiangyu

AU - Chen, Yi

AU - Hu, Xiaozhi

AU - Liu, Wen

AU - Li, Qingbin

AU - Chen, Shougen

PY - 2019/5/14

Y1 - 2019/5/14

N2 - Maximum fracture loads (Pmax)of small notched granite specimens under three-point-bending (3-p-b)conditions can be easily measured with any notch/size ratio. In this study, we report a simple closed-form solution of a non-Linear Elastic Fracture Mechanics (non-LEFM)model emphasizing the influence of average grain size G on quasi-brittle fracture of granite. This simple analytical solution containing the grain size G can be conveniently used to determine granite tensile strength ft and fracture toughness KIC from Pmax measurements of small notched 3-p-b specimens of geometry dissimilarity. The span/width (S/W)ratios of small 3-p-b specimens can vary, e.g. 2.5 or 4. The notch/width (a0/W)can also vary, e.g. the notch a0 can be as short as the average grain size (G), or close to width W. However, specimens with α-ratio (=a0/W)around 0.2 are recommended to minimize the boundary influence/effect from both the front and back specimen boundaries as proven by the Boundary Effect Model (BEM). Blue granite with the average grain size around 2 (mm)was selected to test the new method. Total 64 granite samples from four different groups (different 3-p-b sample designs)were tested, with W = 27, 40 and 70 (mm), S/W = 2.5, 4.0 and a0 = 4, 6 and 8 (mm). The tensile strength ft and fracture toughness KIC estimated from every group is fairly close to the values determined from the entire population of 64 tests. Therefore, tests from any specimen group of given geometry and size are sufficient. Estimations for G = 1.5 and 2.5 (mm)were also provided and compared with those for G = 2 (mm)to show the grain size influence. Advantages and disadvantages of BEM and well-known SEL (size effect law)are also discussed using the granite results.

AB - Maximum fracture loads (Pmax)of small notched granite specimens under three-point-bending (3-p-b)conditions can be easily measured with any notch/size ratio. In this study, we report a simple closed-form solution of a non-Linear Elastic Fracture Mechanics (non-LEFM)model emphasizing the influence of average grain size G on quasi-brittle fracture of granite. This simple analytical solution containing the grain size G can be conveniently used to determine granite tensile strength ft and fracture toughness KIC from Pmax measurements of small notched 3-p-b specimens of geometry dissimilarity. The span/width (S/W)ratios of small 3-p-b specimens can vary, e.g. 2.5 or 4. The notch/width (a0/W)can also vary, e.g. the notch a0 can be as short as the average grain size (G), or close to width W. However, specimens with α-ratio (=a0/W)around 0.2 are recommended to minimize the boundary influence/effect from both the front and back specimen boundaries as proven by the Boundary Effect Model (BEM). Blue granite with the average grain size around 2 (mm)was selected to test the new method. Total 64 granite samples from four different groups (different 3-p-b sample designs)were tested, with W = 27, 40 and 70 (mm), S/W = 2.5, 4.0 and a0 = 4, 6 and 8 (mm). The tensile strength ft and fracture toughness KIC estimated from every group is fairly close to the values determined from the entire population of 64 tests. Therefore, tests from any specimen group of given geometry and size are sufficient. Estimations for G = 1.5 and 2.5 (mm)were also provided and compared with those for G = 2 (mm)to show the grain size influence. Advantages and disadvantages of BEM and well-known SEL (size effect law)are also discussed using the granite results.

KW - Average grain size (G)

KW - Boundary Effect Model (BEM)

KW - Fracture toughness

KW - Granite

KW - Size Effect Law (SEL)

KW - Statistical Scatter

KW - Tensile strength

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