Matrix Cracking In Brittle-Matrix Composites with Tailored Interfaces

1994 ◽  
Vol 365 ◽  
Author(s):  
Sawai Danchaivijit ◽  
L-Y. Chao ◽  
D. K. Shetfty
Keyword(s):  
Steady State ◽  
Crack Length ◽  
Uniaxial Tension ◽  
Sliding Friction ◽  
Crack Opening ◽  
State Theory ◽  
Matrix Cracking ◽  
Opening Displacement ◽  
The Matrix ◽  
Cracking Stress

ABSTRACTMatrix cracking from controlled through cracks with bridging filaments was studied in a model unidirectional composite of SiC filaments in an epoxy-bonded alumina matrix. An unbonded, frictional interface was produced by moderating the curing shrinkage of the epoxy with the alumina filler and coating the filaments with a releasing agent. Uniaxial tension test specimens (2.5 × 25 × 125 mm) with filament-bridged through cracks were fabricated by a novel two-step casting technique involving casting, precracking and joining of cracked and uncracked sections. Distinct matrix-cracking stresses, corresponding to the extension of the filamentbridged cracks, were measured in uniaxial tension tests using a high-sensitivity extensometer. The crack-length dependence of the matrix-cracking stress was found to be in good agreement with the prediction of a fracture-mechanics analysis that employed a new crack-closure force - crack-opening displacement relation in the calculation of the stress intensity for fiber-bridged cracks. The prediction was based on independent experimental measurements of the matrix fracture toughness (Kcm), the interfacial sliding friction stress (τ) and the residual stress in the matrix (σmI). The matrix-cracking stress for crack lengths (2a) greater than 3 mm was independent of the crack length and agreed with the prediction of the steady-state theory of Budiansky, Hutchinson and Evans[2]. Tests on specimens without the deliberately introduced cracks indicated a matrix-cracking stress significantly higher than the steady-state stress.

scholarly journals Non-Steady First Matrix Cracking of Fiber-Reinforced Ceramics

2020 ◽  
Author(s):  
Huan Wang
Keyword(s):  
Steady State ◽  
Crack Opening ◽  
Ceramic Matrix Composites ◽  
Matrix Cracking ◽  
Fiber Direction ◽  
Fiber Reinforced ◽  
Opening Displacement ◽  
Interface Shear ◽  
The Matrix ◽  
Lag Model

Matrix cracking affects the reliability and safety of fiber-reinforced ceramic-matrix composites during operation. The matrix cracking can be divided into two types, that is, steady state crack and non-steady state cracking. This chapter is about the non-steady stable cracking of fiber-reinforced CMCs. The micro stress field of fiber, matrix, and interface shear stress along the fiber direction is analyzed using the shear-lag model. The relationship between the crack opening displacement and the crack surface closure traction is derived. The experimental first matrix cracking stress of different CMCs are predicted.

Mechanics of matrix cracking in brittle-matrix fibre-reinforced composites

1987 ◽  
Vol 409 (1837) ◽  
pp. 329-350 ◽  
Keyword(s):  
Energy Balance ◽  
Crack Opening ◽  
Crack Problem ◽  
Matrix Cracking ◽  
Matrix Composites ◽  
Entire Cross Section ◽  
Brittle Matrix ◽  
Matrix Cracks ◽  
The Matrix ◽  
Cracking Stress

Energy-balance calculations for a continuum model of cracking in a uniaxially fibre-reinforced composite having a brittle matrix are presen­ted. It is assumed that the fibres are strong enough to remain intact when the matrix cracks across the entire cross section of the composite. By equating the energy availability for the cracking of continuum and discrete fibre models it is shown how the crack boundary condition relating fibre stress to crack opening must be selected. It is confirmed that the Griffith fracture criterion is valid for matrix cracking in composites. By considering the energy balance of long cracks it is shown that the limiting value of the stress intensity factor is independent of crack length and that it predicts a matrix-cracking strain that is consistent with the known result. An improved numerical method is described for solving a crack problem arising from the study of the cracking of brittle-matrix composites. Numerical results of high accuracy are obtained, which show how the cracking stress is related to the size of a pre-existing defect. Of special significance is the prediction of the correct threshold stress (i.e. matrix­-cracking stress) below which matrix cracking is impossible no matter how large the pre-existing defect.

System Stiffness and Restraint Effects on Circumferential Crack Opening Displacements: A Rotational Stiffness Approach

2015 ◽  
Author(s):  
Bruce A. Young ◽  
Richard J. Olson
Keyword(s):  
Crack Length ◽  
Structural Model ◽  
Crack Opening ◽  
Local System ◽  
Piping System ◽  
Rotational Stiffness ◽  
Opening Displacement ◽  
Piping Systems ◽  
Conservative Estimation ◽  
Pipe Geometry

Current crack opening displacement (COD) solutions for leak-before-break (LBB) analyses assume the ends of the cracked pipe, which is subjected to remote bending and internal pressure, are free to rotate. However, in plant piping systems, the pressure induced bending and imposed rotations are restrained, because the ends of the pipe are constrained by the rest of the piping system and other components. Hence, existing evaluation procedures, theoretically overestimate the COD values of a circumferential through-wall crack (TWC) in a piping system. These overestimations comprise one of the uncertainties in an LBB analysis, as it leads to an under-prediction of the leakage-size-crack length of a postulated leaking TWC for a prescribed leakage detection limit in a plant, and thus, results in a non-conservative estimation of the crack stability from an LBB perspective. Historical efforts on the effects of restraint on COD have focused on a restraint distance from the crack to restrain the rotation of the pipe. This study provides a fundamentally different approach in that the underlying theory develops a relationship between the apparent rotational stiffness of a pipe with unrestrained ends and the material modulus as a function of crack length and pipe geometry. Thus, the local system stiffness from a plant structural model can be used to modify the unrestrained value of COD.

The Matrix Cracking Stress and Residual Thermal Stress of 2D SiC/SiC Composite Fabricated by PIP Process

2018 ◽  
Vol 281 ◽  
pp. 375-381
Author(s):  
Hai Peng Qiu ◽  
Shan Hua Liu ◽  
Ling Wang ◽  
Bing Yu Zhang ◽  
Ming Wei Chen ◽  
...  
Keyword(s):  
Residual Stress ◽  
Regression Line ◽  
Strain Curve ◽  
Thermal Residual Stress ◽  
Matrix Cracking ◽  
Stress Strain Curve ◽  
Sic Ceramic ◽  
The Matrix ◽  
Sic Composites ◽  
Cracking Stress

A two dimensional silicon carbide fiber reinforced SiC matrix (2D SiC/SiC) composite fabricated by precursor infiltration pyrolysis (PIP) process used a liquid SiC ceramic precursor was obtained. Two key properties including matrix cracking stress and thermal residual stress were investigated for this PIP 2D SiC/SiC composites. Three methods were applied to determine the matrix cracking stress in order to obtained a trusted value, and the value of matrix cracking stress for SiC/SiC composite was 75±4 MPa. The thermal residual stress of the composites was calculated by linear regression line according to the loading-unloading-reloading stress-strain curve of the 2D SiC/SiC composite, and the result showed that the value of thermal residual stress of SiC matrix in composite was 20MPa, which means the PIP SiC matrix in the 2D SiC/SiC composite was under the compressive stress when the composite cooling down from the fabrication temperature to the room temperature.

Anisotropic Media with a Crack or a Rigid Line Inclusion,

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
Crack Opening Displacement ◽  
Crack Opening ◽  
Null Vector ◽  
Opening Displacement ◽  
Rigid Line Inclusion ◽  
Rigid Line ◽  
The Matrix ◽  
Structural Failures ◽  
The Right ◽  
Line Inclusion

A crack, or cracks, in a material is perhaps one of the most studied problems in solid mechanics. This is due to the fact that many structural failures are related to the presence of a crack in the material. The knowledge of stress distribution near a crack tip is indispensable in a fracture mechanics analysis (Rice, 1968; Sih and Liebowitz, 1968; Sih and Chen, 1981; Kanninen and Popelar, 1985; K. C. Wu, 1989a). A crack is represented by a slit cut whose surfaces are assumed traction-free. This is a mathematical idealization. For a composite material that consists of stiff short fibers or whiskers in the matrix, we have rigid line inclusions. A rigid line inclusion is the counterpart of a crack. It is sometimes called an anticrack. The displacement at a rigid line inclusion either vanishes or has a rigid body translation and rotation. One of the puzzling problems for a crack is the one when it is located on the x1-axis that is an interface between two dissimilar materials. The displacement of the crack surfaces near the crack tips may oscillate, creating a physically unacceptable phenomenon of interpenetration of two materials. The bimaterial tensor Š introduced in Section 8.8 plays a key role in the analysis. If Š vanishes identically, there is no oscillation. If Š is nonzero, we may decompose the tractions applied on the crack surfaces into two components, one along the right null vector of Š denoted by to and the other on the right eigenplane of Š denoted by tγ . The solution associated with to is not oscillatory. It has the property that the traction on the interface x2=0 is polarized along the right null vector of Š while the crack opening displacement is polarized along the left null vector of Š. The solution associated with tγ is oscillatory. It has the property that the traction on the interface x2=0 is polarized on the right eigenplane of Š while the crack opening displacement is polarized on the left eigenplane of Š.

Matrix Crack Networks in SiC/SiC Composites: In-Situ Characterisation and Metrics

2021 ◽  
Author(s):  
S. P. Jordan ◽  
S. P. Jeffs ◽  
C. D. Newton ◽  
L. Gale ◽  
P. I. Nicholson ◽  
...  
Keyword(s):  
Crack Opening ◽  
Ceramic Matrix Composites ◽  
Fatigue Loading ◽  
Matrix Crack ◽  
Matrix Cracking ◽  
Damage Development ◽  
Opening Displacement ◽  
Ongoing Research ◽  
Wide Range

Abstract Ceramic matrix composites can offer clear potential for a variety of engineering applications where the temperature capabilities of conventional metals are exceeded. Continued mechanical characterisation is essential to gain an understanding of their associated damage and failure mechanisms across a wide range of representative temperatures. The present paper will report ongoing research to characterize the initiation of matrix cracking at room temperature under tensile stress and subsequent damage development under fatigue loading in a SiCf/SiC composite. Imaging and mechanical property data were obtained via in-situ loading within a scanning electron microscope. The temporal nature of damage development was also recorded through the selective employment of acoustic emission. Metrics to describe the spatial distribution of cracks, crack lengths and crack opening displacement under load will be presented. The inspections also provided detailed evidence of the associated crack closure phenomena. The understanding of matrix crack saturation and matrix/fibre interfacial mechanics will be explored, together with the implications for the use of X-ray tomographic inspection of engineering components during service. The potential for these emergent techniques as a basis for future CMC characterization, via automated image recognition and machine learning, will be highlighted.

Fiber Pullout Characteristics Under Dynamic Loading Conditions

2001 ◽  
Author(s):  
N. Sridhar ◽  
Q. D. Yang ◽  
B. N. Cox
Keyword(s):  
Shear Stress ◽  
Crack Opening ◽  
Interfacial Shear Stress ◽  
Friction Stress ◽  
Crack Plane ◽  
Opening Displacement ◽  
Fiber Pullout ◽  
Dynamic Propagation ◽  
Dependent Relationship ◽  
The Matrix

Abstract Inertial effects in the mechanism of fiber pullout during dynamic propagation of a bridged crack are critically examined. By reposing simple shear lag models of pullout as problems of dynamic wave propagation, the effect of frictional coupling between the fiber and the matrix is accounted for in a fairly straightforward way. The frictional sliding between the fiber and the matrix is described by a constant interfacial friction stress, the sign of which depends on the relative particle velocity of the fiber and the matrix. Analytical solutions are derived when the load or bridging traction on the fiber in the crack plane increases linearly in time. The results show that when the wave speed of the matrix exceeds a critical value, the frictional fiber pullout behavior transitions from a state of pure slip to a state where part of the sliding zone slips and the remaining sticks. When stick occurs, the fiber and the matrix within the stick zone slide past each other with an interfacial shear stress less than the shear stress required for slipping. Regions of slip and stick propagate and increase with time and influence the time-dependent relationship between the crack opening displacement and the bridging tractions.

Prediction of Dynamic Break-Opening Area Under Beyond Design Basis Seismic Loading

2015 ◽  
Author(s):  
M. Uddin ◽  
E. Kurth ◽  
F. W. Brust ◽  
G. M. Wilkowski ◽  
A. A. Betervide ◽  
...  
Keyword(s):  
Crack Length ◽  
Crack Opening Displacement ◽  
Crack Closure ◽  
Crack Opening ◽  
Time History ◽  
Seismic Loading ◽  
Opening Displacement ◽  
Ductile Tearing ◽  
Design Basis ◽  
The Moment

The thermal-hydraulics computer code, RELAP (Reactor Excursion and Leak Analysis Program) is used to analyze loss of coolant accidents (LOCAs) and system transients in PWRs and BWRs. However, RELAP requires the knowledge of break-opening area versus time history for Double-Ended Guillotine Break (DEGB) of a pipe fracture event as an input to calculate pressure drops at critical locations in the primary pipe loop. Previously authors conducted a detailed dynamic FE analyses to determine the condition for DEGB that provided moment versus rotation of the cracked-pipe and time histories for DEGB under beyond design basis seismic loading. In this paper, crack-opening area was calculated using the moment-rotation-time history obtained from dynamic FE analyses. In the LBB.ENG2 J-estimation scheme for circumferentially cracked pipe, the rotation at the cracked-pipe cross-sectional location (rotation due to the crack) is uniquely related to the total crack length and crack-opening displacement at the center of the crack. However, the relationship is only valid when the moment versus rotation from the FE analyses corresponds to the ductile tearing curve from the LBB.ENG2 ductile fracture analysis. During any unloading (and reloading) parts of the applied seismic history, the rotation can drop down from the upper-envelope for the tearing resistance of the cracked pipe in an elastic unloading manner from the seismic/cyclic unloading. During this part of the seismic time-history, the crack length remains constant but the center-crack-opening displacement decreases, i.e., there is crack closure with a constant crack length which needs to be included in predicting crack-opening area. Based on a number of past cyclic pipe fracture tests with large amounts of ductile tearing, a procedure was developed to predict the crack-opening area that included crack closure during cyclic loading of the seismic event. The resulting opening-area versus time history then becomes the input to the RELAP analysis for determination of emergency core cooling/safety processes.

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