Theory Of Fatigue Crack Propagation Research Articles

Lifetime prediction of copper pillar bumps based on fatigue crack propagation

2.5D package realizes the interconnection of multiple dies through Si interposers, which can greatly improve the data transmission rate between dies. However, its multi-layer structure and high package density also place higher reliability requirements on the interconnection structure. As a key structure for interconnection, copper pillar bump (CPB) has small size, high heat generation, and thermal mismatch with silicon chips. The thermal fatigue failure of CPB has gradually become the main failure mode in 2.5D package. Due to the small size of CPB and the large proportion of intermetallic compound (IMC) layers, the lifetime prediction method of spherical solder joints is no longer suitable for CPB. Therefore, it is necessary to establish a fatigue lifetime prediction method for CPB. This paper establishes a method for obtaining the lifetime of CPB based on the basic theory of fatigue crack propagation. Using the extended finite element simulation method, the crack propagation lifetime of CPB under thermal cycling was obtained, and the influence of different IMC layer thickness on the fatigue lifetime of CPB was analyzed. The results indicated that the fatigue lifetime of cracks propagating in the IMC layer is lower than that of cracks propagating in the solder layer, and an increase in the thickness of the IMC layer leads to a significant decrease in the fatigue lifetime of CPB. The lifetime prediction method for CPB proposed in this paper can be used for reliability evaluation of 2.5D package, and has certain reference value for the study of the lifetime of CPB.

Fatigue crack propagation in thin balcony opening corners in a cruise ship accounting for warping deformation

Accurately predicting the fatigue crack propagation (FCP) life of thin balcony opening corner structures with warping deformation using the FCP theory is a major challenging task. Herein, a procedure for analyzing the effect of warping deformation on the FCP in thin balcony opening corner structures is presented. According to the proposed method based on the modesuperposition to simulate the warping deformation (MSSWD), the stress intensity factors (SIFs) of cracks at the midpoint of balcony opening corners with warping deformation are appropriately modified. The FCP tests with reduced-scale models are also performed to provide experimental verification data for the given procedure. The fatigue lives of the specimens under various loads are calculated based on the modified SIFs and unique curve model and then are compared with the test data. The obtained results reveal that this approach can precisely predict the FCP lives of thin balcony opening corners with warping deformation.

Research on breakage characteristics in side milling of titanium alloy with cemented carbide end mill

Titanium alloy Ti6Al4V has the advantages of high specific strength, good heat resistance, and strong corrosion resistance, which is widely used in the manufacturing of aerospace industrial parts. However, in the side milling of titanium alloy, the temperature of the cutting area is high, and the cutting edge position is prone to breakage, which affects the surface quality of the workpiece. In order to reveal the tool damage failure mechanism in the milling process of titanium alloy, firstly, the impact force model when the tool cuts into the workpiece from the empty stroke and the milling force model during milling are established to obtain the cyclic load characteristics and impact effect of the tool. Then, based on the fatigue crack propagation theory and the energy balance equation of sliding crack, the elastic modulus and crack propagation law of tool material under different cutting impacts are analyzed. The interval method is used to recalculate the initial and critical damage value of tool material fracture in the maximum range. Finally, the limit conditions of the edge impact fracture of the end mill are established, and the safe cutting area of tool breakage is redefined. Through the milling test of titanium alloy, the impact damage morphology of tool in different states is redefined. The obtained redefined tool safety area provides a theoretical basis for high-speed and high-efficiency milling of titanium alloy, tool breakage, and tool life.

Fatigue behaviour of corroded stud based on crack growth theory

In order to promote the application and development of steel–concrete composite beams in bridges, the fatigue performance of corroded studs was investigated. Based on fatigue crack propagation theory and the fatigue failure mechanism of corroded studs, a fatigue life prediction model for corroded studs was proposed. The values of key parameters in the fatigue life prediction model of corroded studs were obtained. Moreover, the fatigue life of corroded studs was analysed. Results show that the error between the calculated value and the test value of the fatigue life of corroded studs is less than 10%, and the fatigue life prediction model for corroded studs is sufficiently accurate. As the corrosion rate of a stud increases, its fatigue life rapidly decreases. When the corrosion rate of the stud increases from 5 to 50%, the fatigue life of the stud decreases from 20 to 90%, respectively; thus corrosion greatly reduces the fatigue life of the stud.

Nonlinear Damage Accumulation Rule for Solder Life Prediction Under Combined Temperature Profile With Varying Amplitude

Due to a mismatch of the coefficient of thermal expansion, electronic solder joints experience cyclic shear strain, which ultimately leads to fatigue failure. Traditional predictions of solder joint thermal fatigue life that use the experimental data or the physics-of-failure model often assume a regular profile. For complex temperature profiles, the linear accumulation rule is typically used to integrate the superposition effect. However, the linear rule was proved not applicable to most of the complex loading or temperature conditions. Based on the damage curve theory and the fatigue crack propagation theory, a novel nonlinear accumulation rule has been deduced for solder joint life predictions under irregular profiles, which were composed of two standard temperature cycles and may be experienced by phased-mission system. Four groups of experiments were conducted for ball grid array package solder joints with different dimensions and materials to determine parameters of the proposed nonlinear accumulation rule. The finite-element simulation method was used to extend this rule to more general cases for application. Compared to Miner’s linear accumulation rule, prediction of solder joint thermal fatigue life via the proposed nonlinear accumulation rule is closer to the accelerated life test results of real-world electronic solder joints under a combined temperature profile.

An improved procedure for generating standardised load-time histories for marine structures

The load sequence effect has been proved from laboratory tests to be an influencing factor that cannot be neglected in the fatigue analysis of marine structures. To take account of this significant factor, fatigue life prediction should be based on fatigue crack propagation theory rather than the currently used cumulative fatigue damage theory. Accordingly, fatigue loading needs to be provided as the load-time history in the time domain rather than the load spectrum in the frequency domain. A general procedure for generating the standardised load-time history for marine structures based on a short-term load measurement has been proposed by the authors. This article seeks to further improve on this procedure and explain how to apply the determined standardised load-time history in the fatigue life prediction method based on the fatigue crack propagation theory. Finally, generation and application of a standardised load-time history are given for a tubular T-joint of an offshore platform, which demonstrates the practical and effective use of the proposed approach.

Generation and application of a standardised load-time history to critical ship structural details

Marine structures always experience variable amplitude loading during their service periods. The fatigue crack growth behaviour of marine structures and materials has been proved from laboratory tests to be sensitive to the loading sequence encountered. In order to take account of the load sequence effect, fatigue life prediction should be based on fatigue crack propagation theory rather than the currently used cumulative fatigue damage theory. A unified fatigue life prediction method for marine structures has been developed in the authors’ group. In order to apply the unified fatigue life prediction method for newly designed structures, authorities such as the classification societies should provide a standardised load-time history such as the TWIST and FALSTAFF sequences for transport and fighter aircraft. This paper is mainly aimed to propose a procedure how to generate the standardised load-time history for marine structures based on a short-term load measurement and how to use the resulting standardised load-time history to a critical ship structural detail based on the unified fatigue life prediction method.

On the engineering approach to estimating the parameters in an improved crack growth rate model for fatigue life prediction

Metal structures in ships and offshore platforms are subjected to complex loading histories and one of the most significant failure modes is fatigue. Accurate prediction of the fatigue life of marine structures is very important for both safe and economic design and operation. It has been realised that fatigue crack propagation theory can provide a more rational basis for fatigue strength assessment than traditional cumulative fatigue damage theory. At the same time, more and more fatigue crack growth models are proposed along with a good understanding of metal fatigue mechanisms. In our previous work, a new crack growth rate model extended from the McEvily model was proposed. This model shows promising capability to explain various fatigue phenomena. However, there are still some shortcomings in this model such as the insufficient description of unstable fracture condition and the effect of stress/strain state. At the same time, it is difficult to determine a large number of model parameters without amounts of fatigue test data, which restricts its use in practical engineering problems. In this paper, the model will be further improved first by adopting a continuous empirical formula for estimating the value of variable fracture toughness during crack propagation and introducing a modified continuous equation for the crack tip stress/strain constraint factor used for calculating the stress intensity factor at the opening level. In order to quickly obtain the fatigue crack growth characteristic of a structural element before carrying out enough fatigue tests, the engineering approach to estimating the model parameters by recurring to some research findings on evaluation of fatigue properties was investigated. Based on the engineering approach, costly fatigue tests may be saved and limited tensile or fatigue data will be sufficient for the evaluation of the crack growth rate curve. The prediction results will be proved to agree well with the observed phenomena and results in test.

Approximate method to determine the model parameters in a new crack growth rate model

Marine structures are subjected to complex loading histories and one of the most significant failure modes is fatigue. Accurate prediction of the fatigue life of marine structures is very important for both safe and economic design and operation. Now many researchers and engineers have realized that fatigue crack propagation theory can provide more rational basis to predict the fatigue life of metal structures. At the same time, more and more fatigue crack growth models are proposed along with a good understanding of metal fatigue mechanisms. However, it is difficult to determine a large number of model parameters, which restricts their use in practical engineering problems. Therefore, it is significant to study the approximate methods for estimating the model parameters in good fatigue crack growth models. In our previous work, an extended McEvily model for fatigue crack growth analysis of metal structures was proposed. This model shows promising capability to explain various fatigue phenomena. In order for the convenient use in estimating fatigue life of marine structures, the concepts and approximations of the model parameters are comprehensively studied in this paper. Based on that, more reasonable assumptions and empirical formulas to determine the parameters are recommended. The approximate method is validated by experimental results of several types of materials, which could be successfully used in simple and effective engineering analysis for marine structures.

A feasible study of fatigue life prediction for marine structures based on crack propagation analysis

Marine structures such as ships and offshore platforms are designed with damage tolerance. This requires accurate prediction of fatigue crack growth under service conditions. Current fatigue strength assessment methods for marine structures are largely based on the cumulative fatigue damage (CFD) theory using stress-endurance (S-N) curves. The effects of initial defects and the load sequence have been neglected. The extent of final fatigue failure in real structures is also not specified. These result in a large scatter of the predicted fatigue lives. In the fatigue community, more and more researchers have realized that fatigue crack propagation (FCP) theory could overcome these deficiencies and has the potential to explain various fatigue phenomena observed. In this paper, a feasible study of fatigue life prediction for marine structures based on FCP theory is carried out. The basic requirements and the general procedure for such an analysis are addressed. The feasibility of this procedure and the capabilities of FCP theory for fatigue life prediction are demonstrated using a simple example of a finite width plate with a centre crack subjected to remote uniform fatigue loading. The key problems to be solved for a practical implementation are also discussed.

A global/local theory of fatigue crack propagation

Most fatigue crack propagation studies reported in the literature have been conducted from either a continuum or micro-mechanics point of view. Attempts to combine these points of view within a single experimental study or modeling effort have been relatively scarce. This is surprising considering the global/local nature of the Griffith fracture theory from which modem fracture mechanics theories have emerged. This paper suggests a means of unifying continuum and micro-mechanics approaches by describing fatigue crack propagation processes at both global and local levels in terms of internal energy. By equating the rate of internal energy change as determined from continuum and microstructural models, a fatigue crack propagation rate equation may be obtained which includes parameters descriptive of the fatigue process on both the continuum and microstructural levels.

Application of the crack layer theory of fatigue crack propagation in PMMA

Abstract The crack layer theory has been well established as a good description of the energy dependence of fatigue crack propagation in thermoplastics associated with multiple crazes or large deformation preceding the crack tip. Since PMMA usually displays crack propagation preceded by a single craze, the applicability of the theory in such extreme cases needs to be tested. Fatigue crack propagation data obtained in a previous interferometric investigation in PMMA have been utilized here. Two different approaches are attempted for estimation of the energy dissipated in craze formation and growth. Using both approaches, the crack layer formalism provides a reasonably good description of the crack propagation behavior in PMMA.

A stochastic theory of fatigue crack propagation

A new mathematical theory is proposed to analyze the propagation of fatigue crack based on the concepts of fracture mechanics and random processes. The time-dependent crack size is approximated by a Markov process. Analytical expressions are obtained for the probability distribution of crack size at any given time and the probability distribution of the random time at which a given crack size is reached, conditional on the knowledge of the initial crack size. Examples are given to illustrate the application of the theory, and the results are compared with available experimental data.

低温における780 MPa級高張力鋼溶接各部の疲労き裂伝ぱ特性および疲労破壊靭性

Fatigue test and fracture toughness test in 780 MPa grade high strength steel weldments in the temperature range from 98 K to room temperature were experimentally carried out. Both the tests were performed with a compact tension specimen by using a program-load-controlled 0.98 MN fatigue testing machine.Main results obtained are summarized as follows:(1) The fatigue crack propagation rate in the base metal shows a similar value in both the weld metal and HAZ.(2) The trend of fatigue crack propagation characteristic in weldments in the temperature range from 223 K to room temperature is in good agreement with the dislocation dynamics theory of fatigue crack propagation.(3) Fatigue fracture toughness, Kfc and fracture toughness, Kc in the base metal are larger than in both the weld metal and HAZ.

On the law of fatigue crack layer propagation in polymers

AbstractA generalized theory of fatigue crack propagation in polymers is presented. The theory accounts for crack propagation through root craze extension accompanied by the dissemination of micro defects around the main crack thereby describing a crack layer (CL) system. In addition to the conventional crack length(l), the CL width(w) is introduced as another kinematic parameter. Applying the principle of minimum thermodynamic forces, evolution of l and w is formulated in terms of reciprocal thermodynamic forces. Accordingly the law of Fatigue Crack Layer Propagation (FCLP) is derived in the following dimensionless form where N is the number of cycles, λ ≈ l(N)/l*; l* being the critical CL length, ω = w(l)/w*; w* being the value of w corresponding to l*, β′ and Q′ are energy dissipation and heat evolution functions, respectively. A version of this law provides good description of growth rates from published data.

Generalized theory of fatigue crack propagation: Part I — derivation of thresholds

An energetic analysis of the fatigue crack propagation process has been carried out and it was found that there is a critical effective stress intensity range, ΔK° eff, below which it is energetically unfavorable for a crack front to move continuously normal to itself. It is proposed instead that, below this critical ΔK° eff, the crack front can advance through the lateral motion of ledge-like perturbations on its front in the manner of the low driving force motion of interphase and grain boundaries in phase transformations. Expressions for this critical stress intensity range are derived for noncrystallographic crack fronts and crack fronts suspected to be strongly constrained by crystallographic factors. The magnitudes of these critical stress intensities are discussed with regard to experimentally observed threshold stress intensity ranges.

Generalized theory of fatigue crack propagation: Part II — Derivation of threshold and Paris regime crack growth rates

Expressions for the growth rate of fatigue cracks by the continuous advance of the crack front normal to itself, as well as by the discontinuous ledge-controlled processes, are derived in the presence and absence of strong crystallographic constraints on crack front motion. With no crystallographic constraints, the functional trends found are consistent with the Paris law and the sharply ΔK eff- dependent threshold regime behaviors commonly observed in ductile materials. In the case where strong crystallographic constraints may be operating at all ΔK eff levels, the fatigue crack growth rates derived, based on crack advance rate controlled by the lateral motion of pre-existing ledges on the cusporiented and crystallographic crack front, are proportional to ΔK eff 4 at all ΔK eff levels.

Prediction of endurance of fillet welds subjected to narrow band random loading

Fatigue crack propagation theory is used to predict the performance of cruciform welds subjected to either axial or bending narrow band random loading. The predictions are shown to provide a general representation of two sets of test data. It is concluded that the method enables narrow band random loading fatigue data for welds to be extrapolated to longer endurances.

The effect of frequency on fatigue crack propagation rate and striation spacing in 2024-T3 aluminium alloy and SM-50 steel

The effect of loading frequency on fatigue crack propagation rate and striation spacing in 2024-T3 aluminium alloy and SM-50 steel was studied at room temperature. The fatigue crack propagation rate is expressed experimentally by the equation: dc/dN = AΔK 3ƒ −λ and striation spacing, s by the following formula: s = BΔK 5sƒ −λ , where ƒ= loading frequency, λ = 0.08~0.14 and γ = 0'06~0−12. Fractographical studies were made. The ln dc/ dN− lnΔK straight line and the ln s− lnΔK straight line intersect each other. That is, dc/ dN < s below the stress intensity factor at the intersecting point, and dc/ dN > s above the critical stress intensity factor. It is to be noted that dc/ dN and s will not coincide except the very narrow region near the intersecting point. The formula of dc/ dN experimentally obtained in this article has quite the same type as indicated by the dislocation dynamic theory of fatigue crack propagation.

Fracture toughness and fatigue crack propagation in high strength steel from room temperature to −180°c

Fracture toughness under tensile test and fatigue test on high strength steel at temperature ranging from room temperature to −180°C were experimentally studied. The value of fracture toughness under fatigue test is considerably tower than that obtained under tensile test. Within the range from room temperature to −100°C the following results were obtained: the power coefficient δ of the fatigue crack propagation rate [(dc)/(dN)] = AΔK 5 is related with [(1)/( T)] as: δ = b 1 + [(a 1)/(kT)] . [(dc)/(dN)] shows Arrhenius type, and, however, different equation from usual stress dependent rate process equation. The trend is in good agreement with the dislocation dynamics theory of fatigue crack propagation.