A simple method for predicting the singular stress distribution of Mode I interlamellar crack embedded in unidirectionally-fiber-reinforced composites

Naoya Tada, R. Ohtani, H. Sakurai

Research output: Contribution to journalArticle

Abstract

Elastic-plastic analysis was carried out for a Mode I interlamellar crack embedded in unidirectionally-fiber-reinforced composites by means of the finite element method. The stress distribution in the vicinity of a crack tip was calculated for various crack lengths and various combinations of elastic constants for fiber and matrix. When both fiber and matrix are elastic, the stress intensified region ahead of the crack tip was divided into three regions. In the region nearest the crack tip (Region I), the distribution of stress, σy, which is the normal stress perpendicular to the crack plane, was given by the stress intensity factor, Kcom. Kcom is obtained assuming that the composite is actually composed of two parts which have different elastic constants. On the other hand, the stress distribution in the farthermost part in the stress intensified region was given by the stress intensity factor, Khomo (Region III). Khomo is obtained regarding the composite as homogeneously orthotropic. Between these regions, the stress distribution was undulated (Region II). As Kcom and Khomo can be evaluated analytically using elastic constants of fiber and matrix and Region II always appears at a distance from the crack tip equal to the thickness of matrix, the stress distribution can be predicted without carrying out numerical analyses such as a finite element analysis. When the matrix is assumed to be elastic-perfectly plastic, the length of yield region and the stress outside the yield region can be estimated from the yield stress of the matrix and the stress distribution predicted for the case where the matrix does not yield.

Original languageEnglish
Pages (from-to)524-531
Number of pages8
JournalZairyo/Journal of the Society of Materials Science, Japan
Volume50
Issue number5
Publication statusPublished - May 2001

Fingerprint

stress distribution
Stress concentration
cracks
Cracks
crack tips
composite materials
fibers
Fibers
Crack tips
Composite materials
matrices
Elastic constants
stress intensity factors
elastic properties
Stress intensity factors
plastics
Plastics
Finite element method
Yield stress
finite element method

Keywords

  • Composites
  • Elastic-plastic analysis
  • Finite element method
  • Interlamellar crack
  • Mode I
  • Stress distribution

ASJC Scopus subject areas

  • Chemical Engineering (miscellaneous)
  • Metals and Alloys
  • Polymers and Plastics

Cite this

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title = "A simple method for predicting the singular stress distribution of Mode I interlamellar crack embedded in unidirectionally-fiber-reinforced composites",
abstract = "Elastic-plastic analysis was carried out for a Mode I interlamellar crack embedded in unidirectionally-fiber-reinforced composites by means of the finite element method. The stress distribution in the vicinity of a crack tip was calculated for various crack lengths and various combinations of elastic constants for fiber and matrix. When both fiber and matrix are elastic, the stress intensified region ahead of the crack tip was divided into three regions. In the region nearest the crack tip (Region I), the distribution of stress, σy, which is the normal stress perpendicular to the crack plane, was given by the stress intensity factor, Kcom. Kcom is obtained assuming that the composite is actually composed of two parts which have different elastic constants. On the other hand, the stress distribution in the farthermost part in the stress intensified region was given by the stress intensity factor, Khomo (Region III). Khomo is obtained regarding the composite as homogeneously orthotropic. Between these regions, the stress distribution was undulated (Region II). As Kcom and Khomo can be evaluated analytically using elastic constants of fiber and matrix and Region II always appears at a distance from the crack tip equal to the thickness of matrix, the stress distribution can be predicted without carrying out numerical analyses such as a finite element analysis. When the matrix is assumed to be elastic-perfectly plastic, the length of yield region and the stress outside the yield region can be estimated from the yield stress of the matrix and the stress distribution predicted for the case where the matrix does not yield.",
keywords = "Composites, Elastic-plastic analysis, Finite element method, Interlamellar crack, Mode I, Stress distribution",
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AU - Tada, Naoya

AU - Ohtani, R.

AU - Sakurai, H.

PY - 2001/5

Y1 - 2001/5

N2 - Elastic-plastic analysis was carried out for a Mode I interlamellar crack embedded in unidirectionally-fiber-reinforced composites by means of the finite element method. The stress distribution in the vicinity of a crack tip was calculated for various crack lengths and various combinations of elastic constants for fiber and matrix. When both fiber and matrix are elastic, the stress intensified region ahead of the crack tip was divided into three regions. In the region nearest the crack tip (Region I), the distribution of stress, σy, which is the normal stress perpendicular to the crack plane, was given by the stress intensity factor, Kcom. Kcom is obtained assuming that the composite is actually composed of two parts which have different elastic constants. On the other hand, the stress distribution in the farthermost part in the stress intensified region was given by the stress intensity factor, Khomo (Region III). Khomo is obtained regarding the composite as homogeneously orthotropic. Between these regions, the stress distribution was undulated (Region II). As Kcom and Khomo can be evaluated analytically using elastic constants of fiber and matrix and Region II always appears at a distance from the crack tip equal to the thickness of matrix, the stress distribution can be predicted without carrying out numerical analyses such as a finite element analysis. When the matrix is assumed to be elastic-perfectly plastic, the length of yield region and the stress outside the yield region can be estimated from the yield stress of the matrix and the stress distribution predicted for the case where the matrix does not yield.

AB - Elastic-plastic analysis was carried out for a Mode I interlamellar crack embedded in unidirectionally-fiber-reinforced composites by means of the finite element method. The stress distribution in the vicinity of a crack tip was calculated for various crack lengths and various combinations of elastic constants for fiber and matrix. When both fiber and matrix are elastic, the stress intensified region ahead of the crack tip was divided into three regions. In the region nearest the crack tip (Region I), the distribution of stress, σy, which is the normal stress perpendicular to the crack plane, was given by the stress intensity factor, Kcom. Kcom is obtained assuming that the composite is actually composed of two parts which have different elastic constants. On the other hand, the stress distribution in the farthermost part in the stress intensified region was given by the stress intensity factor, Khomo (Region III). Khomo is obtained regarding the composite as homogeneously orthotropic. Between these regions, the stress distribution was undulated (Region II). As Kcom and Khomo can be evaluated analytically using elastic constants of fiber and matrix and Region II always appears at a distance from the crack tip equal to the thickness of matrix, the stress distribution can be predicted without carrying out numerical analyses such as a finite element analysis. When the matrix is assumed to be elastic-perfectly plastic, the length of yield region and the stress outside the yield region can be estimated from the yield stress of the matrix and the stress distribution predicted for the case where the matrix does not yield.

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