Mechanical Behavior Laboratory University of Nevada, Reno

The Details of Dr. Jiang's Research Accomplishments

Most structural components are subjected to cyclic loading, and fatigue and fracture eventually occur. The majority of the accidents related to mechanical problems, particularly those occurred catastrophically involving in the death of lives, is due to fatigue of the materials. An understanding of fatigue of materials is of critical importance in ensuring the durability and safety of the machines and structures such as power generators, aircraft of all types, cranes, bridges, pipelines, railroads, and pressure vessels. According to a conservative estimation, the annual cost of fatigue of materials and structures to the US economy in 1982 was $100 billion. Such costs reach a total of 4% of the gross national product (GNP) in US.

  • New Multiaxial Fatigue Criterion [J18]

A new and general multiaxial fatigue criterion was developed. The criterion overcomes all the major shortcomings of the existing theories. The model incorporates the critical plane concept in multiaxial fatigue, plastic strain energy, and material memory in cyclic plasticity. With an incremental form the model does not require a cycle counting method for variable amplitude loading. The model is designed to consider mean stress and loading sequence effects.

Verification of the model is made by comparing the predictions obtained by using the new model and experimental data of several engineering materials under various different loading conditions. As shown in Fig.1, excellent correlations were achieved between the experiments and the predictions. Shown in figure includes four different engineering materials under various nonproportional loading paths.

Fig. 1

Fig.1 Comparison of predicted fatigue lives with experimental observations [J18]

Verification of the model is made by comparing the predictions obtained by using the new model and experimental data of several engineering materials under various different loading conditions. As shown in Fig.1, excellent correlations were achieved between the experiments and the predictions. Shown in figure includes four different engineering materials under various nonproportional loading paths.

The multiaxial fatigue criterion was applied to the prediction of polycrystalline and single crystal copper with success [J49, J48, J39, J38]. The criterion serves as the base for the crack growth prediction in the new fatigue life approach [J29].

  • Stress and Fatigue Analyses of Notched Components [J20]

Elastic-plastic stress analysis and fatigue experiments were conducted to evaluate the existing methods for estimating fatigue strength of notched members. The Neuber's rule and its various modifications were found to be applicable to very limited cases.

An elastic-plastic stress analysis was conducted using the finite element method for notched shafts subjected to cyclic axial, torsional, and combined axial-torsion loading. The Jiang-Sehitoglu plasticity model is capable of accurately describing cyclic material behavior and this model was used in the elastic-plastic stress analysis of notched members subjected to proportional and nonproportional loading. The model provides accurate and reliable cyclic stresses and strains for the fatigue analysis of notched members. The approximate methods such as Neuber's method and various modifications based on Neuber's rule for the elastic-plastic stress-strain estimations were critically evaluated with the finite element results. It was concluded that the approximate methods had very limited applications for simple structural geometry and loading conditions.


An innovative approach was developed for the fatigue life predictions of materials and structures subjected to general fatigue loading. The new approach considers both crack initiation and crack growth using one single fatigue criterion. All the material constants are generated from testing smooth material specimens. The approach bridges modeling for different stages of fatigue process.

  • Modeling of Fatigue Crack Growth [J43, J42, J29]

Fatigue crack propagation is modeled by using the cyclic plasticity material properties and fatigue constants for crack initiation. The cyclic elastic-plastic stress-strain field near the crack tip is analyzed using the finite element method with the implementation of a robust cyclic plasticity theory. An incremental multiaxial fatigue criterion is employed to determine the fatigue damage. A straightforward method is developed to determine the fatigue crack growth rate. Crack propagation behavior of a material is obtained without any additional assumptions or fitting. Benchmark Mode I fatigue crack growth experiments were conducted using 1070 steel at room temperature. The approach developed is able to quantitatively capture all the important fatigue crack propagation behaviors including the overload and the R-ratio effects on crack propagation and threshold. The models provide a new perspective for the R-ratio effects. It was confirmed that the fatigue crack initiation and propagation behaviors were governed by the same fatigue damage mechanisms. Crack growth can be treated as a process of continuous crack nucleation. Figure 2 shows the capability of the model to predict crack growth with the R-ratio effect.

Fig. 2

Fig.2 Crack propagation with the effect of R-ratio [J29]

  • Crack Growth from a Notch [J44]

When a fatigue crack is nucleated and propagates into the vicinity of the notch, the crack growth rate is generally higher than that can be expected by using the stress intensity factor concept. The current study attempted to describe the crack growth at notches quantitatively with a detailed consideration of the cyclic plasticity of the material. An elastic-plastic finite element analysis was conducted to obtain the stress and strain histories of the notched component. A single multiaxial fatigue criterion was used to determine the crack initiation from the notch and the subsequent crack growth. Round compact specimens made of 1070 steel were subjected to Mode I cyclic loading with different -ratios at room temperature. The approach developed was able to quantitatively capture the crack growth behavior near the notch. When the R-ratio was positive, the crack growth near a notch was mainly influenced by the plasticity created by the notch and the resulted fatigue damage during crack initiation. When the R-ratio was negative, the contact of the cracked surfaces during a part of a loading cycle reduced the cyclic plasticity of the material near the crack tip. The combined effect of notch plasticity and possible contact of cracked surface were responsible for the observed crack growth phenomenon near a notch. Figure 3 demonstrates the short crack phenomenon observed experimentally and a comparison with the predictions obtained by using the approach developed.

Fig. 3

Fig.3 Experimental crack growth rate and the predicted results (R=-2) [J44]


A localized inhomogeneous cyclic plastic deformation phenomenon was experimentally investigated. Dr. Jiang was the first person who explored the inhomogeneous cyclic plastic deformation with extensive experiments.

Small strain gages were utilized to characterize the local deformation within the gage section and the gross deformation was measured with an extensometer. Both solid specimens and tubular specimens were used. The solid specimens were subjected to both fully reversed symmetrical and asymmetrical loading. Proportional and nonproportional axial-torsion loading conditions were applied to the thin-walled tubular specimens. For stress-controlled tension-compression cyclic loading with the maximum stress lower than the lower yield stress of the material, cyclic plastic deformation is characterized by three stages: incubation, propagation, and saturation (Fig.4). The local strains are significantly inhomogeneous during the propagation stage and the inhomogeneity persists at the saturation stage. The local inhomogeneous cyclic deformation was dependent on the loading magnitude and evolved with continued cyclic loading.

Fig. 4

Fig.4 Variations of local strain amplitudes and propagation of plastic zone with loading cycles for fully reversed stress-controlled loading [J22]

Transmission electron microscopy (TEM) was used to study the microstructures associated with the observed deformation phenomenon. With increasing loading cycles, the dislocation substructures evolved in a sequence of loose tangles, thick veins, long walls, elongated cells, and equiaxial cells. Under cyclic stressing, the dislocations pinned by the Cottrell atmospheres in the ferrite grains are unpinned gradually and become free and mobile dislocations. The movement of free dislocations leads to the multiplication, interaction, and annihilation of dislocations. Dislocation cells are formed at first on the grain boundaries with the activation of multiple slip systems followed by the cells propagation into the interior area of the ferrite grains.


Dr. Jiang's work in self-loosening of bolted joints is a representative example of applying the fundamental research results in solving a long-standing engineering problem.

Bolted joints are the most commonly used components in machines and structures. Often, potential durability problems in a machine or structure are proportional to the number of the bolted joints used. Two failure modes are found in bolted joints subjected to cyclic loading: fatigue and self-loosening. Fatigue is a major failure form for a bolted joint subjected to tensile load and self-loosening is often found in a bolted joint subjected to transverse or shear load. Self-loosening is the gradual loss of the clamping force in the bolted connections under cyclic external loading, especially transverse loading. It can result in a decrease in structural stiffness or the separation of clamped members.

The self-loosening process of a bolted joint consists of two distinct stages. The first stage of self-loosening occurs when there is no relative rotation between the nut and bolt. The second stage of self-loosening is characterized by the backing off of the nut.

  • Study of Early Stage Self-Loosening of Bolted Joints [J25]

Both experimental investigation and finite element analysis were conducted to explore the mechanisms for the early stage self-loosening of bolted joints under transverse cyclic loading. The nuts were glued to the bolts using a strong thread locker in the self-loosening experiments to ensure that no backing-off of the nut occurred. Depending on the loading magnitude, the clamping force reduction ranged from 10% to more than 40% of the initial preload after 200 loading cycles. Three-dimensional elastic-plastic finite element analysis was conducted with the implementation of an advanced cyclic plasticity model. The finite element results revealed that the local cyclic plasticity occurring near the roots of the engaged threads resulted in cyclic strain ratcheting. The localized cyclic plastic deformation caused the stresses to redistribute in the bolt, and the result was the gradual loss of clamping force with loading cycles. The finite element results agreed with the experimental observations quantitatively. When the two clamped plates started to slip and the slip displacement was controlled, both experiments and finite element simulations suggested that the friction between the clamped plates has an insignificant influence on the early stage self-loosening.

  • Study on Second Stage Self-Loosening of Bolted Joints [J47, J27]

Both experiments and theoretical modeling were conducted to study the second stage of self-loosening with the aim to explore the mechanisms responsible for the phenomenon. The experiments mimicked two plates jointed by a bolt and a nut and were subjected to cyclic transverse shear loading. During an experiment, the relative displacement between the two clamped plates was a control parameter. The clamping force, the relative rotation between the nut and the bolt, and the applied transverse load were monitored and recorded for each loading cycle. For a given preload, the relationship between the amplitude of the relative displacement between the two clamped plates and the number of loading cycles to loosening followed a pattern similar to a fatigue curve. There existed an endurance limit below which self-loosening would not persist. A larger preload resulted in a larger endurance limit. However, a large preload increased the possibility for the bolt to fail in fatigue. The results reveal that the use of a regular nut is superior to the use of a flange nut in terms of self-loosening resistance. An endurance diagram concept was developed that can be used directly for the design and evaluation of the bolted joints. An engineering model was developed for the relationship between the cyclic transverse load and the relative displacement between the two clamped plates.

Fig. 5

Fig.5 Three-dimensional mesh model for finite element analysis of bolted joint [J47]

A three-dimensional finite element (FE) model with the consideration of the helix angle of the threads was developed to explore the mechanisms of the second stage self-loosening of a bolted joint (Fig.5). It was found that due to the application of the cyclic transverse load, micro-slip occurred between the contacting surfaces of the engaged threads of the bolt and the nut. In addition, a cyclic bending moment was introduced on the bolted joint. The cyclic bending moment resulted in an oscillation of the contact pressure on the contacting surfaces of the engaged threads. The micro-slip between the engaged threads and the variation of the contact pressure were identified to be the major mechanisms responsible for the self-loosening of a bolted joint. Simplified finite element models were developed that confirmed the mechanisms discovered. The major self-loosening behavior of a bolted joint can be properly reproduced with the FE model developed. The results obtained from the finite element simulations agree quantitatively with the experimental observations (Fig.6).

Fig. 6a

Fig.6(a) Comparison of FE predictions with experimental clamping force reduction: Early stage self-loosening [J25]

Fig. 6b

Fig.6(b) Comparison of FE predictions with experimental clamping force reduction: Second stage self-loosening [J47]

  • Effect of Clamped Length and Loading Direction on Self-Loosening [J40]

Many factors influence the performance of a bolted joint. An experimental investigation was conducted to study the effects of clamped length and loading direction on self-loosening of bolted joints. Specially designed fixtures were used for the study. The joints were subjected to cyclic external loading. The reduction in clamping force, the applied transverse load, and the nut rotation were measured cycle by cycle. The relationship between the amplitude of the relative displacement between the two clamped plates and the number of loading cycles to loosening is referred to as self-loosening curve and was obtained for different clamped lengths and applied load directions. It was found that increasing the clamped length can enhance the self-loosening endurance limits in terms of the controlled relative displacement of the two clamped plates. However, the load carrying capability was not influenced significantly due to the thickness of the clamped plates. For a given bolted jointed structure, an angle of the external load from the pure shearing direction resulted in an increase in self-loosening resistance.


Cyclic plasticity deals with the nonlinear stress-strain response of a material subjected to repeated external loading. It is a part of the broad and fascinating subject of continuum mechanics, which spans the spectrum from the fundamental aspects of elastic and inelastic behavior to the practical solution of engineering problems. Plastic deformation is difficult to avoid in many design situations and cyclic plastic deformation often results in fatigue failure. The elastic-plastic stress-strain response plays a pivotal role in the design and failure analyses of many components in practical applications. The ability to model inelastic deformation is of practical interest in many design applications, particularly with the current emphasis on lighter weight structures and components.

  • Experimental Exploration of Cyclic Ratcheting Phenomena [J2, J3]

Critical experiments were initiated and conducted for exploring new ratcheting phenomena. Ratcheting rate decay with a power law relationship was found. Ratcheting was found to be dependent on the loading path under nonproportional loading. Material displays a strong memory of the previous loading history. Ratcheting direction can be opposite to the mean stress direction. The experimental results provide a great challenge for the constitutive modeling of plasticity.

Cyclic ratcheting refers to progressive and directional plastic deformation when a material is subjected to an asymmetric stress-controlled cycling. Figure 7 illustrates this phenomenon for 1070 steel [J3]. In the first loading step with a positive mean stress, the axial strain ratchets in the direction of the mean stress. The ratchetting rate, i.e., the ratcheting strain per loading cycle, decreases with increasing loading cycles and it follows a power law relation with the number of loading cycles. When the mean stress is reduced in Step 2 but keeping a positive value, the strain ratchets in the negative direction opposite to the mean stress. The material exhibits a strong memory of the previous loading history, and such memory plays a discerning role on the subsequent ratcheting. I was the first person to explore the material memory effect that results in the inconsistent ratcheting direction with the mean stress direction.

Fig. 7

Fig.7 Experimental cyclic ratcheting for a two-step uniaxial loading [J3]. Note the ratchetting rate decay in Step 1 and the inconsistency of ratchetting direction with mean stress in Step 2

Extensive ratcheting experiments were conducted under various proportional and nonproportional loading paths. It was found that under nonproportional loading, the ratchetting direction was determined by the loading path and can be different from the mean stress direction. As shown in Fig.8 for a nonproportional axial-torsion loading path (stress-controlled loading path shown in the up-right corner of the figure), the shear stress is fully reversed. However, the strain ratchets in the shear direction even though there is no mean stress in the shear stress direction [J2].

Fig. 8

Fig.8 Ratcheting under nonproportinal axial-torsin loading [J2]

  • Critical Evaluation of Existing Cyclic Plasticity Models [J9, J8, J6]

By using the experimental results, the existing cyclic plasticity models were critically evaluated. Two types of constitutive models, multiple surface such as proposed by Mroz and Garud, and the Armstrong-Frederick type as modified by Chaboche et al were critically evaluated. It was found that the Armstrong-Frederick type models are superior to the Mroz type models. Multiple surface and the associated two surface models with a stationary bounding surface have both theoretical and numerical problems for nonproportional loading paths. The Armstrong-Frederick class of models demonstrate a diminished sensitivity to modeling parameters, as well as a single-valued stress-strain representation for both severe nonproportional loading paths. The Chaboche model predicts constant ratcheting rate as contrast persistent ratcheting rate decay found in the experiments. The model proposed by Jiang and Sehitoglu was found to be the best in the existing models for the prediction of long-term ratcheting deformation under both proportional and nonproportional loading conditions.

  • New Cyclic Plasticity Model [J10, J11]

A new plasticity model was developed. The model can account for most cyclic plasticity behaviors experimentally observed including an accurate description of ratchetting rate decay.

The new model incorporates an Armstrong-Frederick type hardening rule and the concept of a limiting surface for the backstress. To represent the transient behavior, the model encompasses a memory surface in the deviatoric stress space which recalls the maximum stress level of prior loading history. The non-Masing behavior and stress level effect on cyclic ratchetting are realized with the size of the introduced memory surface. The new model predicts long term ratchetting rate decay as well as constant ratchetting rate for both proportional and nonproportional loadings. The theoretical predictions obtained using the new plasticity model are compared with a number of multiple step ratchetting experiments under both uniaxial and biaxial tension-torsion stress states. Very close agreements are achieved between the experimental results and the model simulations. Figure 9 show a comparison of the predicted ratcheting rate and the experimental observations. The axial-torsion loading path followed an apple-shaped path as shown in Fig.8. Clearly, the predictions agree with the experimental results very well for very long loading cycles. A notable characteristic of the new model is its ability to predict long term ratchetting rate decay. The model can also mimic such experimental phenomena as ratchetting in the direction opposite to mean stress under multiple step proportional loading and ratchetting direction change during a constant amplitude loading.

Fig. 9

Fig.9 Comparison of the predicted ratcheting results with experimental observations [J11]

Work has been also done to evaluate the characteristics of the new hardening rule, invoking both theoretical and experimental considerations. The model is insensitive to the yield stress chosen. Numerical extrapolation of the cyclic stress-strain curve can enhance modeling without any penalty. The additional material constants employed to model ratchetting have a minimal influence on either proportional or nonproportional balanced loading, hence these terms can be considered to be decoupled. All these factors indicate the engineering potential of the model. Furthermore, the basic structure of the model is amenable to incorporation of other material behaviors such as non-Masing, cyclic hardening or softening, and nonproportional hardening.

  • Nonproportional Hardening [J13]

Benchmark experiments were conducted to investigate the nonproportional hardening behavior of several materials and the capability of the existing models for describing nonproporitonal hardening was critically evaluated. An improved model was developed.

Fig. 10

Fig.10 Nonproportional hardening of 304 stainless steel under axial-torsion loading [J13]

Nonproportional hardening refers to the additional resistance of a material to plastic deformation due to nonproportional loading. As shown in Fig.10, the stress response of the 304 stainless steel is much higher under nonproportional loading than proportional loading. Amplitude dependence of the hardening is observed. It was found that the method by Marquis et al by using a variable characterizing the change of loading direction was not adequate for describing nonproportional hardening. In view of the existing parameters for describing the nonproportional hardening, the one proposed by Tanaka shows the most promise. A model incorporating the four order tensor parameter proposed by Tanaka was developed for describing nonproportional hardening for various loading conditions. The new model predicts nonproportional hardening results in favorable agreement with the experimental observations (Fig.10).

  • Cyclic Transient Plasticity Behavior [J14]

Both experimental study and theoretical modeling were conducted to investigate the cyclic transient behavior of materials.

Proportional cyclic hardening and non-Massing behaviors were studied. The interaction of these two hardenings can result in the traditionally observed overall softening, hardening or mixed behavior exhibited for fully reversed strain controlled fatigue tests. Proportional experiments were conducted with five materials, 304 stainless steel, normalized 1045 and 1070 steels, 7075-T6 and 6061-T6 aluminum alloys. All the materials display similar trends, but the 304 stainless steel shows the most pronounced transient behavior. Existing algorithms for this behavior are evaluated in light of the experiments, and refinements to the Jiang-Sehitoglu plasticity model are proposed. Implications of the deformation characteristics with regard to fatigue life estimation, especially variable amplitude loading, are examined. The high-low step loading is utilized to illustrate the effect of transient deformation on fatigue life estimation procedures, and their relationship to the observed and modeled deformation.

  • Cyclic Plasticity Model for Single Crystals [J28]

The Armstrong-Frederick type kinematic hardening rule was invoked to capture the Bauschinger effect of the cyclic plastic deformation of a single crystal. The yield criterion and flow rule were built on individual slip systems. Material memory was introduced to describe strain range dependent cyclic hardening. The experimental results of copper single crystals were used to evaluate the cyclic plasticity model. It was found that the model was able to accurately describe the cyclic plastic deformation and properly reflect the dislocation substructure evolution. The well-known three distinctive regimes in the cyclic stress-strain curve of the copper single crystals oriented for single slip can be reproduced by using the model. The model can predict the enhanced hardening for crystals oriented for multislip, showing the ability of model to describe anisotropic cyclic plasticity. For a given loading history, the model was able to capture not only the saturated stress-strain response but also the detailed transient stress-strain evolution. The model was used to predict the cyclic plasticity under a high-low loading sequence. Both the stress-strain responses and the microstructural evolution can be appropriately described through the slip system activation. Figure 11 shows a comparison of the theoretical results with the experimental observations for the single crystal copper oriented for single slip under fully reversed cyclic loading.

Fig. 11a

Fig.11(a) Cyclic stress-strain hysteresis loops for single crystal copper oriented for single slip [J28]: Experiment

Fig. 11b

Fig.11(b) Cyclic stress-strain hysteresis loops for single crystal copper oriented for single slip [J28]: Simulation


Rolling contact can be found in many applications such as roller bearings, gears, tires, and rails and wheels. When the contact load exceeds the plastic shakedown limit, continuous cyclic plastic deformation occurs near the contact surface. The cyclic deformation promotes microstructure changes and results in failure of a rolling element in the forms of crack initiation, crack growth, and fragmentation. It is evident that the near-surface plastic deformation contributes to the sliding wear and the initiation of contact fatigue cracks. As a particular example, rolling contact fatigue of rails is a severe and growing problem in the world.

  • A New Method for Rolling Contact Stress Analysis [J4, J1]

Based on a stress invariant hypothesis and a stress/strain relaxation procedure, an analytical approach is developed for approximate determination of residual stresses and strain accumulation in elastic-plastic stress analysis of rolling contact. For line rolling contact problems, the method produces residual stress distributions in favorable agreement with the existing finite element findings. It constitutes a significant improvement over the Merwin-Johnson and McDowell-Moyar methods established earlier. The approach is employed to study combined rolling and sliding for selected materials. It was found that normal load determines the subsurface residual stresses and the size of the subsurface plastic zone. On the other hand, the influence of tangential force penetrates to a depth of 0.3a, where a is the half width of the contact area, and has diminishing influence on the residual stresses beyond this thin layer. Furthermore, the calculated residual stresses are compared with the existing experimental data from the literature with exceptional agreements.

Together with the Jiang-Sehitoglu cyclic plasticity model, further study of rolling contact revealed that the ratchetting rate of rolling surface movement rapidly decreases with increasing number of rolling passages and ratchetting continues for many cycles. The simulations confirm that a driven wheel undergoes enhanced fatigue damage compared to a driving wheel. It is concluded that the pure rolling contact produces "forward" surface movement. The tangential force plays a considerable role in the surface ratchetting but its influence on the residual stresses is insignificant. The overall residual stresses are mainly determined by the magnitude of the contact pressure.

  • Elastic-Plastic Finite Element Stress Analysis of Rolling Contact [J31, J24, J23]

The finite element model with the implementation of a robust cyclic plasticity theory was used to simulate the elastic-plastic stresses for the partial slip (stick-slip) line rolling contact and three dimensional rolling contact. Detailed rolling contact stresses and strains were obtained for up to 40 rolling passes. The partial slip condition greatly affects the residual stress in the rolling direction and the residual shear strain within a thin layer of material near the contact surface. The residual stress in the axial direction was not significantly influenced by the partial slip condition. An increase in friction coefficient drives the location of maximum shear strain to the contact surface. In addition, a comparison was made between the finite element results and the results obtained from an approximate method. The Jiang-Sehitoglu semi-analytical approach can provide results close to the finite element results for line rolling contact problems.

Three-dimensional elastic-plastic finite element simulations were conducted to study the influences of the tangential surface forces in the two shear directions on residual stresses and residual strains. Residual stresses increase with increasing rolling passes but tend to stabilize. Residual strains also increase but the increase in residual strain per rolling pass decays with rolling cycles. Residual stress levels can be significantly high. Local accumulated shear strains can exceed 20 times the yield strain in shear after six rolling passes under extreme conditions.

  • New Failure Model for Rolling Contact [J16]

Rolling contact stress and failure analyses were conducted for two different alloys. A series of fatigue experiments were conducted on these alloys to establish the damage parameters. A critical plane fatigue damage parameter was used. Maximum local plastic strains, accumulated strains, and three dimensional residual stresses were computed under pure rolling conditions. The Jiang-Sehitoglu plasticity model was used in the calculations of the contact stress and strain fields. The advantage of this model over the previous models is that it predicts the correct trends in the material ratcheting rate and non-proportional loading response. For life prediction, a new combined ratchetting-multiaxial fatigue damage model was developed. The damage at different depths below the surface was interrogated with this model to determine the location where failure will originate. The results show that the Bainitic alloy exhibits longer lives under the same Hertzian pressure and for both materials the life is finite when the normalized pressure, ratio, exceeded 4.0.