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Review Articles

Size Effect Law and Critical Distance Theories to Predict the Nominal Strength of Quasibrittle Structures

[+] Author and Article Information
Pere Maimí

Associate Professor
e-mail: pere.maimi@udg.edu

Emilio V. González

Assistant Professor
e-mail: emilio.gonzalez@udg.edu

Narcís Gascons

Associate Professor
e-mail: narcis.gascons@udg.edu

Lluís Ripoll

Associate Professor
e-mail: lluis.ripoll@udg.edu
AMADE, Polytechnic School,
Universitat de Girona,
Campus Montilivi s/n,
Girona 17071, Spain

Manuscript received August 6, 2012; final manuscript received March 12, 2013; published online May 23, 2013. Editor: Harry Dankowicz.

Appl. Mech. Rev 65(2), 020803 (May 23, 2013) (16 pages) Paper No: AMR-12-1037; doi: 10.1115/1.4024163 History: Received August 06, 2012; Revised March 12, 2013

The design of structures with a nonuniform stress field is of great industrial interest. The ability of the size effect law and critical distance theories to predict the nominal strength of notched and open hole specimens is analyzed in the present paper. The results obtained with these methods are compared with the solution of the problem computed, taking into account the material cohesive law. A conclusion of this paper is that the role of the critical fracture energy in determining the structural strength is negligible, except in large cracked structures. For unnotched structures of any size and for small cracked structures, the key parameter is the initial part of the softening cohesive law. This allows us to define design charts that relate the structural strength to a specimen size normalized with respect to a material characteristic length.

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Figures

Grahic Jump Location
Fig. 1

(a) Notched and open hole specimen and (b) size effect law on structural strength

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Fig. 2

Description of a failure process zone when a crack is progressing and constitutive law relations

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Fig. 3

Failure process zone of a fiber composite

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Fig. 4

Nominal strength according to the SEL for cracked (r = 2) and holed specimens with r = 2 and r = 1

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Fig. 5

Influence of the Weibull statistics in the size effect law: Eq. (7) for α = 1 and α = 0.1 and nD/nW = 1/10 and nD/nW = 1/20

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Fig. 6

Nominal strength of the cracked specimen according to the PSM, ASM, IFM, FFM, and DBM

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Fig. 7

Nominal strength of the holed specimen according to the PSM, ASM, IFM, FFM, and DBM

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Fig. 8

Strip yield model for the open hole specimen

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Fig. 9

Stress profile at failure plane for a given length of the FPZ. The nominal strength is defined when the sign of stress at point A changes from negative to positive.

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Fig. 10

Nominal strength of the cracked specimen according to CDT combinations with variable characteristic length

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Fig. 11

Nominal strength of the holed specimen according to CDT combinations with variable characteristic length

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Fig. 12

Open hole specimen with a failure process zone as a superposition of n + 1 linear problems

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Fig. 13

Constant and linear cohesive laws

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Fig. 14

Nominal strength and length of the FPZ for the cracked (gray) and open hole (black) specimens with a constant and a linear cohesive law

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Fig. 15

Crack opening displacement at maximum load for the cracked (gray) and holed (black) specimens for a linear cohesive law

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Fig. 16

Bilinear cohesive laws

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Fig. 17

Bilinear cohesive laws (a) normalized by means of the total fracture energy (GC) and (b) by means of the first part of the cohesive law expressed by the initial fracture energy (GCI)

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Fig. 18

Nominal strength and crack opening displacement of the cracked and open hole specimens for the cohesive laws shown in Fig. 17 normalized with the critical fracture energy

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Fig. 19

Nominal strength and crack opening displacement of the cracked and open hole specimens for the cohesive laws shown in Fig. 17 normalized with the initial fracture energy

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