An Interpretation of the Mechanics of Crack Growth by Fatigue

1965 ◽  
Vol 87 (1) ◽  
pp. 230-236 ◽  
Author(s):  
B. Cotterell
Keyword(s):  
Brittle Fracture ◽  
Crack Propagation ◽  
Crack Length ◽  
Crack Growth ◽  
Driving Force ◽  
Maximum Stress ◽  
High Strength ◽  
Crack Driving Force

A theory for the growth of cracks by fatigue is developed that is analogous to the brittle fracture of high strength materials. It is argued that it is possible to describe crack growth with a curve of resistance which is dependent on the alternating stress at low rates of crack propagation. At higher rates there is much less dependency on the alternating stress. Once such curves have been prepared the rate of crack growth can be found from the value of the crack driving force. This force is dependent mainly on the maximum stress and crack length.

The Effects of Constraint and Compressive or Tensile Residual Stresses on Brittle Fracture

2009 ◽  
Author(s):  
Simon Kamel ◽  
Robert C. Wimpory ◽  
Michael Hofmann
Keyword(s):  
Fracture Toughness ◽  
Residual Stress ◽  
Brittle Fracture ◽  
Driving Force ◽  
High Strength ◽  
Element Analysis ◽  
Crack Driving Force ◽  
Temperature Fracture ◽  
Crack Tip Constraint ◽  
Two Parameter

Residual stress is a key feature in components containing defects which can affect the crack driving force and alter the crack tip constraint to give a modified fracture toughness. In this paper experimental and numerical investigations are performed on ‘C’ shape fracture mechanics specimens, extracted from a high strength low alloy tubing steel, to examine the effects of constraint and tensile or compressive residual stress on brittle fracture. The residual stress is introduced into the specimens by a tensile or compressive mechanical pre-load to produce, respectively, a compressive or tensile residual stress in the region where the crack is introduced. Neutron diffraction measurements are performed on the pre-loaded specimens prior to introduction of a crack, and compared with predictions of the residual stress from finite-element analysis, using tensile properties derived at room temperature. Fracture toughness tests are carried out on the as-received (non-preloaded) and pre-loaded specimens and the effect of residual stress on crack driving force and constraint is evaluated using the two-parameter J-Q approach.

scholarly journals Crystallographic crack propagation rate in single-crystal nickelbase superalloys

2018 ◽  
Vol 165 ◽  
pp. 13012
Author(s):  
Christian Busse ◽  
Frans Palmert ◽  
Paul Wawrzynek ◽  
Björn Sjödin ◽  
David Gustafsson ◽  
...  
Keyword(s):  
Finite Element ◽  
Crack Propagation ◽  
Crack Growth ◽  
Driving Force ◽  
Crack Propagation Rate ◽  
Propagation Rate ◽  
Mode I ◽  
Force Parameter ◽  
Intensity Factors ◽  
Crack Driving Force

Single-crystal nickel-base superalloys are often used in the hot sections of gas turbines due to their good mechanical properties at high temperatures such as enhanced creep resistance. However, the anisotropic material properties of these materials bring many difficulties in terms of modelling and crack growth prediction. Cracks tend to switch cracking mode from Mode I cracking to crystallographic cracking. Crystallographic crack growth is often associated with a decrease in crack propagation life compared to Mode I cracking and this must be taken into account for reliable component lifing. In this paper a method to evaluate the crystallographic crack propagation rate related to a crystallographic crack driving force parameter is presented. The crystallographic crack growth rate is determined by an evaluation of heat tints on the fracture surface of a specimen subjected to fatigue loading. The complicated crack geometry including two crystallographic crack fronts is modelled in a three dimensional finite element context. The crack driving force parameter is determined by calculating anisotropic stress intensity factors along the two crystallographic crack fronts by finite-element simulations and post-processing the data in a fracture mechanics tool that resolves the stress intensity factors on the crystallographic slip planes in the slip directions. The evaluated crack propagation rate shows a good correlation for both considered crystallographic cracks fronts.

scholarly journals Molecular Dynamics Simulation of Crack Propagation in Single-Crystal Aluminum Plate with Central Cracks

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Jun Ding ◽  
Lu-sheng Wang ◽  
Kun Song ◽  
Bo Liu ◽  
Xia Huang
Keyword(s):  
Molecular Dynamics ◽  
Plastic Deformation ◽  
Crack Propagation ◽  
Strain Rate ◽  
Single Crystal ◽  
Crack Length ◽  
Crack Growth ◽  
Plastic Yield ◽  
Model Size ◽  
Dislocation Multiplication

The crack propagation process in single-crystal aluminum plate (SCAP) with central cracks under tensile load was simulated by molecular dynamics method. Further, the effects of model size, crack length, temperature, and strain rate on strength of SCAP and crack growth were comprehensively investigated. The results showed that, with the increase of the model size, crack length, and strain rate, the plastic yield point of SCAP occurred in advance, the limit stress of plastic yield decreased, and the plastic deformability of material increased, but the temperature had less effect and sensitivity on the strength and crack propagation of SCAP. The model size affected the plastic deformation and crack growth of the material. Specifically, at small scale, the plastic deformation and crack propagation in SCAP are mainly affected through dislocation multiplication and slip. However, the plastic deformation and crack propagation are obviously affected by dislocation multiplication and twinning in larger scale.

Unification proposals for fatigue crack propagation laws

2017 ◽  
Vol 13 (2) ◽  
pp. 262-283 ◽  
Author(s):  
Vladimir Kobelev
Keyword(s):  
Differential Equation ◽  
Crack Propagation ◽  
Crack Length ◽  
Closed Form ◽  
Crack Growth ◽  
Stress Ratio ◽  
Elementary Functions ◽  
Content Type ◽  
Number Of Cycles ◽  
Cycles To Failure

Purpose The purpose of this paper is to propose the new dependences of cycles to failure for a given initial crack length upon the stress amplitude in the linear fracture approach. The anticipated unified propagation function describes the infinitesimal crack-length growths per increasing number of load cycles, supposing that the load ratio remains constant over the load history. Two unification functions with different number of fitting parameters are proposed. On one hand, the closed-form analytical solutions facilitate the universal fitting of the constants of the fatigue law over all stages of fatigue. On the other hand, the closed-form solution eases the application of the fatigue law, because the solution of nonlinear differential equation turns out to be dispensable. The main advantage of the proposed functions is the possibility of having closed-form analytical solutions for the unified crack growth law. Moreover, the mean stress dependence is the immediate consequence of the proposed law. The corresponding formulas for crack length over the number of cycles are derived. Design/methodology/approach In this paper, the method of representation of crack propagation functions through appropriate elementary functions is employed. The choice of the elementary functions is motivated by the phenomenological data and covers a broad region of possible parameters. With the introduced crack propagation functions, differential equations describing the crack propagation are solved rigorously. Findings The resulting closed-form solutions allow the evaluation of crack propagation histories on one hand, and the effects of stress ratio on crack propagation on the other hand. The explicit formulas for crack length over the number of cycles are derived. Research limitations/implications In this paper, linear fracture mechanics approach is assumed. Practical implications Shortening of evaluation time for fatigue crack growth. Simplification of the computer codes due to the elimination of solution of differential equation. Standardization of experiments for crack growth. Originality/value This paper introduces the closed-form analytical expression for crack length over number of cycles. The new function that expresses the damage growth per cycle is also introduced. This function allows closed-form analytical solution for crack length. The solution expresses the number of cycles to failure as the function of the initial size of the crack and eliminates the solution of the nonlinear ordinary differential equation of the first order. The different common expressions, which account for the influence of the stress ratio, are immediately applicable.

scholarly journals Low-Cycle Fatigue Crack Growth in Ti-6242 at Elevated Temperature

2014 ◽  
Vol 891-892 ◽  
pp. 422-427 ◽  
Author(s):  
Rebecka Brommesson ◽  
Magnus Hörnqvist ◽  
Magnus Ekh
Keyword(s):  
Crack Length ◽  
Crack Growth ◽  
Low Cycle Fatigue ◽  
High Strength ◽  
Cycle Fatigue ◽  
Load Drop ◽  
Actual Measure ◽  
Smooth Bars ◽  
Number Of Cycles ◽  
The Relationship

During low-cycle fatigue test with smooth bars the number of cycles to initiation is commonly defined from a measured relative drop in aximum load. This criterion cannot be directly related to the actual measure of interest - the crack length. By relating data from controlled crack growth tests under low-cycle fatigue conditions of a high strength Titanium alloy at 350°C and numerical simulation of these tests, it is shown that it is possible to determine the relationship between load drop and crack length, provided that care is taken to consider all relevant aspects of the materials stress-strain response.

A research on fatigue crack growth monitoring based on multi-sensor and data fusion

2019 ◽  
pp. 147592171986572
Author(s):  
Chang Qi ◽  
Yang Weixi ◽  
Liu Jun ◽  
Gao Heming ◽  
Meng Yao
Keyword(s):  
Finite Element ◽  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Data Fusion ◽  
Crack Propagation ◽  
Finite Element Model ◽  
Crack Length ◽  
Crack Growth ◽  
Lamb Wave ◽  
Element Model

Fatigue crack propagation is one of the main problems in structural health monitoring. For the safety and operability of the metal structure, it is necessary to monitor the fatigue crack growth process of the structure in real time. In order to more accurately monitor the expansion of fatigue cracks, two kinds of sensors are used in this article: strain gauges and piezoelectric transducers. A model-based inverse finite element model algorithm is proposed to perform pattern recognition of fatigue crack length, and the fatigue crack monitoring experiment is carried out to verify the algorithm. The strain spectra of the specimen under cyclic load in the simulation and experimental crack propagation are obtained, respectively. The active lamb wave technique is also used to monitor the crack propagation. The relationship between the crack length and the lamb wave characteristic parameter is established. In order to improve the recognition accuracy of the crack propagation mode, the random forest and inverse finite element model algorithms are used to identify the crack length, and the Dempster–Shafer evidence theory is used as data fusion to integrate the conclusion of the two algorithms to make a more accountable and correct judge of the crack length. An experiment has been conducted to demonstrate the effectiveness of the method.

scholarly journals Short fatigue crack growth in welded joints described by the effective cyclic J-integral

2018 ◽  
Vol 165 ◽  
pp. 09002
Author(s):  
Désiré Tchoffo Ngoula ◽  
Michael Vormwald
Keyword(s):  
Fatigue Crack ◽  
Fatigue Life ◽  
Fatigue Crack Growth ◽  
Residual Stresses ◽  
Crack Growth ◽  
Welded Joints ◽  
Driving Force ◽  
J Integral ◽  
Crack Driving Force ◽  
Short Fatigue Crack

The purpose of the present contribution is to predict the fatigue life of welded joints by using the effective cyclic J-integral as crack driving force. The plasticity induced crack closure effects and the effects of welding residual stresses are taken into consideration. Here, the fatigue life is regarded as period of short fatigue crack growth. The node release technique is used to perform finite element based crack growth analyses. For fatigue lives calculations, the effective cyclic J-integral is employed in a relation similar to the Paris (crack growth) equation. For this purpose, a specific code was written for the determination of the effective cyclic J-integral for various lifetime relevant crack lengths. The effects of welding residual stresses on the crack driving force and the calculated fatigue lives are investigated. Results reveal that the influence of residual stresses can be neglected only for large load amplitudes. Finally, the predicted fatigue lives are compared with experimental data: a good accordance between both results is achieved.

A Fatigue Crack Driving Force Parameter

2008 ◽  
Author(s):  
Ying Xiong ◽  
Zengliang Gao ◽  
Junichi Katsuta ◽  
Takeshi Sakiyama
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Driving Force ◽  
Crack Tip ◽  
Force Model ◽  
Crack Driving Force ◽  
R Ratio ◽  
Two Parameter ◽  
Better Than

Most of the previous parameters that utilized as a crack driving force were established in modifying the parameter Kop in Elber’s effective SIF range (ΔKeff = Kmax–Kop). This paper focuses on the physical meaning of compliance changes caused by plastic deformation at the crack tip, the test was carried out for structural steel under constant amplitude loading, and differences of several parameter ΔKeff in literature are analyzed quantificationally. The effect of actual stress amplitude at the crack tip on fatigue crack growth is investigated, and improved two-parameter driving force model ΔKdrive(=Kmax)n(ΔK^)1−n) has been proposed. Experimental data for several different types of materials taken from literature were used in the analyses. Presented results indicate that the parameter ΔKdrive is equally effective or better than ΔK(=Kmax-Kmin), ΔKeff(=Kmax-Kop) and ΔK*(=(Kmax)α(ΔK+)1−α) in correlating and predicting the R-ratio effects on fatigue crack growth rate.

Sign in / Sign up

Export Citation Format

Share Document