Measurements of the velocity of crack propagation in glass plates

1963 ◽  
Vol 53 (1) ◽  
pp. 87-93
Author(s):  
John DeNoyer ◽  
Henry Pollack
Keyword(s):  
Crack Propagation ◽  
Energy Distribution ◽  
Strain Energy ◽  
Crack Velocity ◽  
Crack Path ◽  
Velocity Of Propagation ◽  
Glass Plates

Abstract The velocity of crack propagation in glass plates has been measured. The plates were strained until fractures were initiated. Measurements made over various small segments of the crack path show variations in crack velocity from 0.01 to about 4 km/sec. The velocity of propagation appears to be related to the strain-energy distribution. Regions of the plate where the strain energy was high prior to fracture yielded the highest crack velocities.

scholarly journals SIMULATION OF CRACK PROPAGATION IN TWO DIMENSIONAL PROBLEMS

2010 ◽  
Vol 13 (4) ◽  
pp. 40-50
Author(s):  
Thien Tich Truong ◽  
Bang Kim Tran
Keyword(s):  
Crack Propagation ◽  
Strain Energy ◽  
Crack Path ◽  
Maximum Energy ◽  
Rate Theory ◽  
Stress Theory ◽  
Crack Trajectory ◽  
Minimum Strain Energy ◽  
Maximum Energy Release ◽  
Strain Energy Density Theory

Predicting crack trajectory when crack propagation occurs plays an important role in fracture mechanics problems because this will evaluate whether important areas of structure are heavily influenced by crack propagation. This article will introduce three theories to predict crack path, including maximum tangential stress theory, maximum energy release rate theory and minimum strain energy density theory. Besides, the FRANC2D program is used to simulate the crack propagation based on three above theories.

scholarly journals Crack Propagation in the Human Bone. Mode I of Fracture

2018 ◽  
Vol 26 (2) ◽  
pp. 59-70
Author(s):  
E. M. Craciun ◽  
A. Rabaea ◽  
M. F. Popa ◽  
C. I. Mihailov
Keyword(s):  
Crack Propagation ◽  
Strain Energy ◽  
Maximum Stress ◽  
Crack Path ◽  
Hilbert Problem ◽  
Mathematical Problem ◽  
Human Bone ◽  
Mode I ◽  
Crack Faces ◽  
Stress Criteria

Abstract The problem of crack propagation in human bone is studied. We for- mulate and solve the mathematical problem for the pre-stressed crack in Mode I of classical fracture. Using the boundary conditions on the crack faces in the bone, regarded as an elastic composite material, we solve our Riemann-Hilbert problem. Using generalized Sih's strain energy density generalized and maximum stress criteria we find the direction of the crack path in Iliac bone, regarded as a pre-stressed orthotropic composite.

scholarly journals Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

2021 ◽  
Author(s):  
Javier Bonet ◽  
Antonio J. Gil
Keyword(s):  
Kinetic Energy ◽  
Crack Propagation ◽  
Mathematical Models ◽  
Linear Elasticity ◽  
Strain Energy ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Discontinuous Solutions ◽  
Linear Elasticity Theory ◽  
Intersonic Crack Propagation

AbstractThis paper presents mathematical models of supersonic and intersonic crack propagation exhibiting Mach type of shock wave patterns that closely resemble the growing body of experimental and computational evidence reported in recent years. The models are developed in the form of weak discontinuous solutions of the equations of motion for isotropic linear elasticity in two dimensions. Instead of the classical second order elastodynamics equations in terms of the displacement field, equivalent first order equations in terms of the evolution of velocity and displacement gradient fields are used together with their associated jump conditions across solution discontinuities. The paper postulates supersonic and intersonic steady-state crack propagation solutions consisting of regions of constant deformation and velocity separated by pressure and shear shock waves converging at the crack tip and obtains the necessary requirements for their existence. It shows that such mathematical solutions exist for significant ranges of material properties both in plane stress and plane strain. Both mode I and mode II fracture configurations are considered. In line with the linear elasticity theory used, the solutions obtained satisfy exact energy conservation, which implies that strain energy in the unfractured material is converted in its entirety into kinetic energy as the crack propagates. This neglects dissipation phenomena both in the material and in the creation of the new crack surface. This leads to the conclusion that fast crack propagation beyond the classical limit of the Rayleigh wave speed is a phenomenon dominated by the transfer of strain energy into kinetic energy rather than by the transfer into surface energy, which is the basis of Griffiths theory.

Nonlinear Approach for Strain Energy Release Rate in Micro Cantilevers

2010 ◽  
Author(s):  
Arash Kheyraddini Mousavi ◽  
Seyedhamidreza Alaie ◽  
Maheshwar R. Kashamolla ◽  
Zayd Chad Leseman
Keyword(s):  
Surface Roughness ◽  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Rigid Substrate ◽  
Micro Cantilever

An analytical Mixed Mode I & II crack propagation model is used to analyze the experimental results of stiction failed micro cantilevers on a rigid substrate and to determine the critical strain energy release rate (adhesion energy). Using nonlinear beam deflection theory, the shape of the beam being peeled off of a rigid substrate can be accurately modeled. Results show that the model can fit the experimental data with an average root mean square error of less than 5 ran even at relatively large deflections which happens in some MEMS applications. The effects of surface roughness and/or debris are also explored and contrasted with perfectly (atomically) flat surfaces. Herein it is shown that unlike the macro-scale crack propagation tests, the surface roughness and debris trapped between the micro cantilever and the substrate can drastically effect the energy associated with creating unit new surface areas and also leads to some interesting phenomena. The polysilicon micro cantilever samples used, were fabricated by SUMMIT V™ technology in Sandia National Laboratories and were 1000 μm long, 30 μm wide and 2.6 μm thick.

scholarly journals The influence of edge effects on crack propagation in snow stability tests

2014 ◽  
Vol 8 (1) ◽  
pp. 229-257
Author(s):  
E. H. Bair ◽  
R. Simenhois ◽  
A. van Herwijnen ◽  
K. Birkeland
Keyword(s):  
Crack Propagation ◽  
Strain Energy ◽  
Wave Speed ◽  
Strain Energy Release Rate ◽  
Field Tests ◽  
Strain Energy Release ◽  
Element Model ◽  
Fe Model ◽  
Test Length ◽  
Column Tests

Abstract. Propagation tests are used to assess the likelihood of crack propagation in a snowpack, yet little is known about how test length affects propagation. Guidelines suggest beams with lengths around 1 m for Extended Column Tests (ECTs) and Propagation Saw Tests (PSTs). To examine how test length affects propagation, we performed 163 ECTs and PSTs 1 to 10 m long. On days with full crack propagation in 1.0 to 1.5 m tests, we then made videos of tests 2 to 10 m long. We inserted markers for particle tracking to measure collapse amplitude, collapse wave speed, and wavelength. We also used a finite element model to simulate the strain energy release rate at fixed crack lengths. We find that: (1) the proportion of tests with full propagation decreased with test length; (2) collapse was greater at the ends of the beams than in the centers; (3) collapse amplitudes in the longer tests were consistent with the shorter tests and did not reach a constant value; (4) collapse wavelengths in the longer tests were around 3 m, 2 × greater than what is predicted by the anticrack model. Based on our field tests and FE models, we conclude that the shorter tests fully propagated more frequently because of increased stress concentration from the far edge. The FE model suggests this edge effect occurs for PSTs up to 2 m long or a crack to beam length ratio ≥ 0.20. Our results suggest that ECT and PST length guidelines may need to be revisited.

Fractographic Investigations of Ordinary Ceramic Refractory Materials with Reduced Brittleness

2009 ◽  
Vol 409 ◽  
pp. 209-215 ◽  
Author(s):  
Harald Harmuth ◽  
Christian Manhart
Keyword(s):  
Correlation Length ◽  
Strain Energy ◽  
Crack Path ◽  
Elastic Strain Energy ◽  
Maximum Load ◽  
Refractory Materials ◽  
Group Of Seven ◽  
Large Size ◽  
Surface Profiles ◽  
Ceramic Refractory

A fractographic procedure was developed and applied for ordinary ceramic refractory materials with a rather large size of heterogeneities and defects. It is based on a stereooptical method for generation of digital surface profiles which are evaluated by an autocorrelation function. Furthermore, a lateral correlation length is derived. A group of seven refractory materials was characterised by mechanical and fracture mechanical investigations, and the same specimens had been characterized by the fractographic procedure. Correlations have been tested. The results show a relation between the lateral correlation length and two fracture mechanical characteristics which are significant for the material brittleness and the elastic strain energy stored at maximum load. These relations are contributed to the dependence of the crack path on brittleness. With decreasing brittleness the amount of the crack path proceeding along the grain/matrix boundary increases for the materials investigated.

scholarly journals Phase-field modeling of fracture in heterogeneous materials: jump conditions, convergence and crack propagation

2020 ◽  
Author(s):  
Arne Claus Hansen-Dörr ◽  
Jörg Brummund ◽  
Markus Kästner
Keyword(s):  
Crack Propagation ◽  
Phase Field ◽  
Strain Energy ◽  
Heterogeneous Media ◽  
Phase Field Model ◽  
Diffuse Interface ◽  
Jump Conditions ◽  
Modeling Framework ◽  
Material Interfaces ◽  
Mechanical Jump Conditions

Abstract In this contribution, a variational diffuse modeling framework for cracks in heterogeneous media is presented. A static order parameter smoothly bridges the discontinuity at material interfaces, while an evolving phase-field captures the regularized crack. The key novelty is the combination of a strain energy split with a partial rank-I relaxation in the vicinity of the diffuse interface. The former is necessary to account for physically meaningful crack kinematics like crack closure, the latter ensures the mechanical jump conditions throughout the diffuse region. The model is verified by a convergence study, where a circular bi-material disc with and without a crack is subjected to radial loads. For the uncracked case, analytical solutions are taken as reference. In a second step, the model is applied to crack propagation, where a meaningful influence on crack branching is observed, that underlines the necessity of a reasonable homogenization scheme. The presented model is particularly relevant for the combination of any variational strain energy split in the fracture phase-field model with a diffuse modeling approach for material heterogeneities.

Dynamic Property and Fatigue Crack Propagation Research on Tire Sidewall and Model Compounds

1985 ◽  
Vol 58 (4) ◽  
pp. 785-805 ◽  
Author(s):  
D. G. Young
Keyword(s):  
Fatigue Crack ◽  
Crack Propagation ◽  
Strain Rate ◽  
Fatigue Crack Propagation ◽  
Strain Energy ◽  
Laboratory Data ◽  
Sample Thickness ◽  
Strain Level ◽  
Strain Rate Effects ◽  
Rate Effects

Abstract Research was conducted to define appropriate compound loading conditions and energy parameters required to properly control and analyze fatigue crack propagation experiments for tire sidewall applications. The effects of strain level, pulse frequency, overall cycle frequency, sample thickness, and oven temperature were screened, and strain level was shown to be the dominant variable in the region of interest. Designed experiments further confirmed that frequency (i.e., strain rate) effects upon strain energy are small at normal rates of tire deformation (equivalent to 40 Hz). However, at typical laboratory test frequencies (≤5 Hz), strain rate effects on strain energy are large, and the differences vs. results under tire conditions depend heavily on polymer type as well as test temperature. Thus, the use of strain level, strain rate, and temperature conditions which simulate the tire service environment are critical to give representative results in laboratory testing. A constitutive equation was defined which provides an excellent model for strain energy in pure (or simple) shear as a function of the principal extension ratio (i.e., strain level) at constant frequency. Therefore, computer modeling of such experiments appears straightforward using an on-line minicomputer. Fatigue crack propagation studies showed major effects of pure-shear sample thickness, processing prior to molding, different types of reference compounds, and different polymer types. Halobutyl compounds and halobutyl/EPDM/NR blends were shown to provide superior FCP resistance at a given strain or strain energy level. These results were consistent with earlier tire and laboratory data.

Fatigue Crack Propagation in New Generation Aluminium Alloys

2011 ◽  
Vol 488-489 ◽  
pp. 476-479
Author(s):  
Sébastien Richard ◽  
Christine Sarrazin-Baudoux ◽  
Jean Petit
Keyword(s):  
Fatigue Crack ◽  
Crack Propagation ◽  
Fatigue Crack Propagation ◽  
Alloy Composition ◽  
Crack Path ◽  
Aging Condition ◽  
Modelling Framework ◽  
Alloy Type ◽  
New Generation ◽  
Atmosphere Environment

The fatigue crack propagation behaviour of a new third generation Al-Cu-Li alloy type 2050-T84 developed for aeronautical applications is studied in comparison to a new generation Al-Cu-Mg alloy type 2022-T851. The alloy resistance against crack growth is shown to depend on alloy composition, aging condition and atmosphere environment. The crack path and the growth rate at moderate DK and in the near-threshold domain are discussed in terms of the slip morphology with respect to the microstructure. The different crack propagation regimes, as identified by mean of micro-fractographic observations and EBSD analysis are discussed on the basis of a modelling framework elaborated for conventional metallic alloys.

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