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 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.

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.

Crack Growth Characteristics of Pure Copper for Smart Stress Memory Patch

2007 ◽  
Vol 353-358 ◽  
pp. 2045-2048
Author(s):  
Shoichi Nambu ◽  
Manabu Enoki
Keyword(s):  
Crack Propagation ◽  
Crack Length ◽  
Crack Growth ◽  
Stress Amplitude ◽  
Pure Copper ◽  
Growth Behavior ◽  
Growth Characteristics ◽  
Crack Growth Behavior ◽  
Stress Memory ◽  
The Relationship

A new sensing method called “smart stress memory patch”, which could estimate the maximum stress, the stress amplitude and the fatigue cyclic number simultaneously using Kaiser effect of Acoustic Emission (AE) and crack length of this patch, was developed. In this study, the crack growth characteristics of this patch was evaluated. Pure copper was used for this patch because its good corrosion resistance, stable crack propagation and so on. Two kinds of samples which were rolled and electrodeposited copper were prepared to investigate the effect of microstructure on crack growth behavior. Fatigue test was performed under constant stress amplitude to evaluate the crack growth behavior using the relationship between stress intensity factor range and crack propagation rate. The scattering in fatigue crack growth was also investigated to obtain the relationship between crack length and the fatigue cyclic number including two-sided 95% confidence interval. The effect of thickness and grain size on the scattering was discussed. Finally, good crack growth behavior was obtained and the fatigue cyclic number could be estimated by this patch.

Environment-Assisted Cracking of Zr-Based Bulk Metallic Glass

2007 ◽  
Vol 561-565 ◽  
pp. 1279-1282 ◽  
Author(s):  
Yoshikazu Nakai ◽  
Makoto Seki ◽  
Yasunori Yoshioka
Keyword(s):  
Cyclic Loading ◽  
Metallic Glass ◽  
Crack Propagation ◽  
Crack Growth ◽  
Bulk Metallic Glass ◽  
Stress Ratio ◽  
Deionized Water ◽  
Sustained Load ◽  
Loading Frequency ◽  
Nacl Solution

Crack propagation tests on a bulk metallic glass, Zr55Cu30Ni5Al10, were conducted either in aqueous sodium chloride (NaCl) solutions or deionized water. Crack growth experiments were conducted under cyclic loading at a stress ratio of 0.1 or 0.5 under a loading frequency of 20 or 1.0 Hz. The experiments were also conducted under a sustained load. Although the crack growth rate in deionized water was almost identical to that in air, the rate in NaCl solution was much higher than that in air even in a very low concentration of NaCl such as 0.01%. In 3.5% NaCl solution, the time-based crack propagation rate during cyclic loading, da/dt, was determined by the maximum stress intensity factor, Kmax, but was independent of the loading frequency and the stress ratio, and the rate was almost identical to that of environment-assisted cracking under a sustained load.

Fatigue analysis of groove weld with steel bar backing by fracture mechanics finite elements

1988 ◽  
Vol 15 (4) ◽  
pp. 524-533 ◽  
Author(s):  
Farid Taheri ◽  
Aftab A. Mufti
Keyword(s):  
Finite Element ◽  
Fracture Mechanics ◽  
Stress Ratio ◽  
Stress Range ◽  
Cyclic Life ◽  
Linear Elastic ◽  
Steel Bar ◽  
Elastic Fracture ◽  
Number Of Cycles ◽  
Cycles To Failure

The purpose of this paper is to analyze the fatigue crack growth rate in groove weld with backing steel bar. The linear elastic fracture mechanics approach is used. This approach is coded in a special purpose fracture mechanics package FAST. By using FAST, the structure is modeled and analyzed by its finite element module FAST-I, and the cyclic life is estimated by its crack propagation module FAST-II.An example recently studied by Baker and Kulak is investigated by the FAST program. The S–N curve (stress range versus number of cycles to failure) obtained by FAST is compared with the curve presented by Baker and Kulak. Key words: Engineering, finite element, fracture mechanics, fatigue, steel, stress intensity factor, numerical, computer analysis, weld, stress ratio, enriched element.

Effect fracture resistance on retardation of crack growth

2015 ◽  
Vol 6 (4) ◽  
pp. 510-521
Author(s):  
Jirí Behal ◽  
Petr Homola ◽  
Roman Ružek
Keyword(s):  
Fatigue Crack ◽  
Stress Intensity ◽  
Fatigue Crack Growth ◽  
Crack Propagation ◽  
Aluminium Alloy ◽  
Crack Growth ◽  
Stress Intensity Factors ◽  
High Stress ◽  
Intensity Factors ◽  
Content Type

Purpose – The prediction of fatigue crack growth behaviour is an important part of damage tolerance analyses. Recently, the author’s work has focused on evaluating the FASTRAN retardation model. This model is implemented in the AFGROW code, which allows different retardation models to be compared. The primary advantage of the model is that all input parameters, including those for an initial plane-strain state and its transition to a plane-stress-state, are objectively measured using standard middle-crack-tension M(T) specimens. The purpose of this paper is to evaluate the ability of the FASTRAN model to predict correct retardation effects due to high loading peaks that occur during variable amplitude loading in sequences representative of an aircraft service. Design/methodology/approach – This paper addresses pre-setting of the fracture toughness K R (based on J-integral J Q according to ASTM1820) in the FASTRAN retardation model. A set of experiments were performed using specimens made from a 7475-T7351 aluminium alloy plate. Loading sequences with peaks ordered in ascending-descending blocks were used. The effect of truncating and clipping selected load levels on crack propagation behaviour was evaluated using both experimental data and numerical analyses. The findings were supported by the results of a fractographic analysis. Findings – Fatigue crack propagation data defined using M(T) specimens made from Al 7475-T7351 alloy indicate the difficulty of evaluating the following two events simultaneously: fatigue crack increments after application of loads with maximum amplitudes that exceeded J Q and subcritical crack increments caused by loads at high stress intensity factors. An effect of overloading peaks with a maximum that exceeds J Q should be assessed using a special analysis beyond the scope of the FASTRAN retardation model. Originality/value – Measurements of fatigue crack growth on specimens made from 7475 T7351 aluminium alloy were carried out. The results indicated that simultaneously evaluating fatigue crack increments after application of the load amplitude above J Q and subcritical increments caused by the loads at high stress intensity factors is difficult. Experiments demonstrated that if the fatigue crack reaches a specific length, the maximal amplitude load induces considerable crack growth retardation.

Reliability estimation for aluminum alloy welded joint with automatic image measurement of surface crack growth

2016 ◽  
Vol 33 (4) ◽  
pp. 1205-1223 ◽  
Author(s):  
Qizi Huang Peng ◽  
Tianyu Liu ◽  
Quan Sun ◽  
Wenwei Huang
Keyword(s):  
Crack Length ◽  
Aluminium Alloy ◽  
Crack Growth ◽  
Welded Joints ◽  
Welded Joint ◽  
Reliability Estimation ◽  
Monitor System ◽  
Growth Data ◽  
Image Measurement ◽  
Content Type

Purpose – As an important connecting component, the reliability of aluminium alloy welded joints influences the whole structural effectiveness and stability of equipment. The purpose of this paper is to propose a novel reliability estimation approach to the welded joints based on time-transformed Wiener process with automatic image measurement of crack growth. The crack length information of the welded joints is incorporated into reliability analysis to reflect the product time-varying characteristics. Design/methodology/approach – The proposed approach is superior to other crack growth estimations in that it innovatively introduce a non-contact and flexible photogrammetry technique.First, on-line crack growth images of aluminium alloy welded joints are acquired by the designed monitor system. Second, crack length is calculated with image measurement, then the crack growth data during the manufacturing process is prepared. Finally, a time-transformed Wiener process is used to modeling the degradation, and reliability estimation is carried out with Wiener model. The approach has been validated on five 7075-T7351 welded joint samples. Findings – The method has a twofold task: first, the extraction of crack length growth data by a sequence of image processing. The main step is to model the crack skeleton with crack skeleton tree, and remove it edges to calculate the length of crack; second, the prediction of crack growth and reliability estimation. Research limitations/implications – The limitation of proposed method should not be ignored. The pixel/mm scale should be calibrated in advance that means once we have built the monitor system, the relative position of the CCD camera and the surveyed crack cannot change anymore. It has reduced the flexibility. To improve this, we can obtain binocular vision in crack image measurement. The 3-D measurements could solve calibration problem and provide more information, such as the depth and the orientation of crack to research. Therefore, future work can be centered on the improvement of monitor system and measurement precision. Originality/value – In the paper a novel method to estimate reliability of crack growth from welded joint based on image measurement has been presented. This method could be widely applied in different filed of manufacturing systems, reliability engineering and structural analysis.

Numerical simulation of fatigue crack propagation in mixed-mode (I+II) using the program BemCracker2D

2019 ◽  
Vol 10 (4) ◽  
pp. 497-514
Author(s):  
Pedro G.P. Leite ◽  
Gilberto Gomes
Keyword(s):  
Numerical Simulation ◽  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Fracture Mechanics ◽  
Crack Propagation ◽  
Crack Growth ◽  
Mixed Mode ◽  
Mode I ◽  
Post Processing ◽  
Content Type

Purpose The purpose of this paper is to present the application of the boundary element method (BEM) in linear elastic fracture mechanics for analysis of fatigue crack propagation problems in mixed-mode (I+II) using a robust academic software named BemCracker2D and its graphical interface BemLab2D. Design/methodology/approach The methodology consists in calculating elastic stress by conventional BEM and to carry out an incremental analysis of the crack extension employing the dual BEM (DBEM). For each increment of the analysis, the stress intensity factors (SIFs) are computed by the J-Integral technique, the crack growth direction is evaluated by the maximum circumferential stress criterion and the crack growth rate is computed by a modified Paris equation, which takes into account an equivalent SIF to obtain the fracture Modes I and II. The numerical results are compared with the experimental and/or BEM values extracted from the open literature, aiming to demonstrate the accuracy and efficiency of the adopted methodology, as well as to validate the robustness of the programs. Findings The paper addresses the numerical simulation of fatigue crack growth. The main contribution of the paper is the introduction of a software for simulating two-dimensional fatigue crack growth problems in mixed-mode (I+II) via the DBEM. The software BemCracker2D coupled to the BemLab2D graphical user interface (GUI), for pre/post-processing, are very complete, efficient and versatile and its does make relevant contributions in the field of fracture mechanics. Originality/value The main contribution of the manuscript is the development of a GUI for pre/post-processing of 2D fracture mechanics problems, as well as the object oriented programming implementation. Finally, the main merit is of educational nature.

Study on Fatigue Crack Propagation at Negative Stress Ratio in 2A12 Aluminum Alloy

2011 ◽  
Vol 335-336 ◽  
pp. 809-812
Author(s):  
Shi Gang Bai ◽  
Jia Zhen Zhang ◽  
Yu Sha
Keyword(s):  
Aluminum Alloy ◽  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Propagation ◽  
Crack Growth ◽  
Fatigue Crack Propagation ◽  
Stress Ratio ◽  
Compressive Loading ◽  
Stress Cycle ◽  
Made In

This paper intends to get compressive loading effect on fatigue crack growth of 2A12 aluminum alloy. The fatigue crack propagation tests at negative stress ratio R=-0.5, -1and -2 were made in different applied compressive loading. The result showed that the effect of the compressive loading part of the applied stress cycle on fatigue crack growth rate in 2A12 aluminum alloy at negative stress ratio can not be omitted.

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