Residual Stress Intensity Research Articles

Effect of plug on levelling of residual stress in tube drawing

The effect of a plug on residual stress in tube drawing is examined by both numerical analysis and laboratory experiment. In the numerical analysis, finite element method is applied to study the residual stress in tube drawing both with and without a plug. Under the condition that a plug is not used, the axial residual stress is analyzed changing the tube wall thickness. The axial residual stress pattern is almost the same regardless of the wall thickness, and it is tensile near the outer surface and compressive near the inner surface. Based on the results, the mechanism of residual stress generation is assumed and a certain reduction in thickness by a plug is envisaged to be effective for levelling of the residual stress. It is thought that the residual stress would be levelled more efficiently with the increase of reduction in thickness, though the drawing force would increase at the same time. Therefore, it is important to find the minimum bare reduction in thickness to level the residual stress. Successively, a series of numerical experiments was carried out to decide the effective range of thickness reduction by a plug. In order to evaluate the intensity of residual stress, an index, which is the integration of the absolute value of axial residual stress, was introduced. As a result, it is revealed that a certain minimum bare thickness reduction exists, beyond which the intensity of the residual stress is significantly reduced. In order to verify the result of numerical analysis, experiments were also conducted using a drawing machine. In the experiments, the intensity of residual stress was evaluated by a slitting method where the tubes were divided into eight pieces by slitting every 45° and the displacements of the tube ends were measured. The numerical and experimental results are in good agreement.

Evaluation of Residual Stresses During Fatigue Test in an FSW Joint

Abstract: This paper shows an application of the adjusted compliance ratio method (ACR), and the on‐line crack‐compliance technique for determination of the effects of the residual stress during a fatigue test. The fatigue crack growth tests were carried out on a friction stir welded (FSW) joint in Ti‐6Al‐4V titanium alloy. On‐line crack compliance enables the determination of the residual stress intensity factor in real time from a fatigue test. The ACR methodology was used to separate the residual stress effects from the crack growth rate data. Finally, the residual stress distribution of the FSW joint was found from the knowledge of the residual stress intensity factor through an integral solution. It would have to be noted that both methods are based on ratios of displacements; therefore, the practical application does not require the use of the influence functions needed for the cut‐compliance method. Moreover, a specific test, which determines residual stresses, can be avoided because the effect of the same residual stresses on the crack growth is evaluated during the fatigue test. This methodology is more accurate than cut compliance because it reflects the real crack growth behaviour.

Residual Stress Evaluation of AA2024-T3 Friction Stir Welded Joints

The main aim of this study was to evaluate the residual stress field in friction stir welded joints of 2024-T3 aluminum alloy plates using the slitting method. This is based on the fact that when a cut, simulating a growing crack, is incrementally introduced into a part, residual stresses are relieved on the slot surfaces created, causing the part to deform. Such deformation can be measured by strain gages attached to specific regions of the part and the residual stress profile that originally existed can be evaluated. Cuts were introduced by wire electro discharge machining (WEDM), in finishing mode, either perpendicularly or longitudinally to the weld nugget, in 3.2 × 60 × 120 mm3 rectangular testpieces. For the longitudinal testpieces, the slot was introduced in two different positions: on the center of the weld nugget and 5 mm distant from the weld center line, in order to sample the thermomechanically/heat affected zone. The residual stress intensity factor, K r, was calculated using a fracture mechanics approach and the inverse weight function method was employed to obtain the initial residual stress profile. Residual stress redistribution profiles ahead of the slot tip could also be derived using the inverse weight function method. However, for cracked components subjected to compressive residual stress fields, when the crack faces are in contact, a non-linear problem arises and the zero displacement condition has to be taken into account in order to provide a more accurate solution of the residual stress field.

An Elastic-Plastic Thermal Stress Analysis of Cross-ply and Angle-ply Aluminum Metal-matrix Composite Arches

A thermal elastic-plastic stress analysis is carried out on cross-ply and angle-ply steel fiber reinforced aluminum metal-matrix laminated composite arch under uniform temperature distribution. The composite material is assumed to be strain hardening linearly and consists of 4, 8, 12, and 16 layers bonded symmetrically and anti-symmetrically. First yielding temperature, thermal residual stresses, and the distribution of these stresses under thermal loading are investigated by using the finite element method (FEM). The effects of orientation angle, layer number, and stacking sequence on the residual stresses are analyzed. The magnitudes of residual stress components increase gradually depending on the temperature increment. It is found that the orientation angle affects the yield point and the intensity of residual stresses significantly, while the layer number and stacking sequence result in slight differences.

Fatigue Life Prediction of Ship Welded Materials

Fatigue crack propagation life of weld toe crack through residual stress field was estimated using Elber's crack closure concept. Propagation of weld toe crack is heavily influenced by residual stresses caused by the welding process, so it is essential to take into account the effect of residual stresses on the propagation life of a weld toe crack. Fatigue cracks at transverse and longitudinal weld toe was studied, these two cases represent the typical weld joints in ship structures. Numerical and experimental studies are performed for both cases. Residual stresses near the welding area were estimated through a nonlinear thermo-elasto-plastic finite element method and the residual stress intensity factor with Glinka's weight function method. Effective stress intensity factor was calculated using the Newman-Forman-de Koning-Henriksen equation, which is based on the Dugdale strip yield model in estimating the crack closure level, U, at different stress ratios. Calculated crack propagation life coincided well with experimental results.

A Study on the Buckling Behaviour of Strips and Plates with Residual Stresses

During and after rolling or flattening of metal strips and plates the permissible deviations from flatness are described by the permissible absolute wave height and the flatness index. Both values can be determined on a measuring table while the material is not subjected to global tension. Because this procedure is expensive, time‐consuming and allows measurement only at discrete positions along the strip length, on‐line flatness measuring systems are used which can detect the distribution of longitudinal tensile stresses distributed across the strip width allowing for the calculation of the flatness index. This value does not always agree with the value obtained directly by measuring on the table even when the measurement of the longitudinal tensile stress distribution operates perfectly. It can be shown that the measurement of the tensile stress distribution does not give a direct indication on the wave height in the tension‐free state determined on the measuring table.To explain the relationship between tensile stress distribution in the strip and the flatness measurement on the measuring table, the buckling behavior is analysed both with and without dead load for simple symmetrical residual stress distributions resulting, e.g., from the rolling process. Based on the knowledge of the distribution of the longitudinal residual stresses across the strip width, the flatness index and the wave height can be determined by using a specialized finite element model. If the direct measurement is performed under action of dead load, large differences between the directly and indirectly obtained flatness index are observed. Below a certain limit of the intensity of the residual stress distribution the strips and plates lie flat on the measuring table. Above this limit the strip lying on the table exhibits post‐bucking deformations. In the latter case, the wave height increases with strip thickness and intensity of residual stresses.

配管端部から円周溶接部までの距離が残留応力と応力拡大係数に及ぼす影響 溶接残留応力場におけるSCCき裂進展評価（第１報）

配管端部から円周溶接部までの距離が残留応力と応力拡大係数に及ぼす影響 溶接残留応力場におけるSCCき裂進展評価（第１報）

Residual Stresses and Stress Intensity Factors for Vickers Indentation Cracks in Glass Derived from COD Measurements

Vickers indentation cracks are an appropriate tool to determine the crack‐tip toughness KI0 of brittle materials as ceramics from the total crack opening displacements. In addition, the residual stresses occurring in the surrounding of an indentation can be evaluated. The fracture mechanics procedure is described in detail and applied to indentation cracks in glass.

A threshold stress intensity factor at the onset of stable crack extension of Knoop indentation cracks

Observation of the stable growth of indentation cracks in controlled bending tests is an attractive tool to study the R-curve behaviour of ceramic materials. In some crack growth experiments deviations from the ideal behaviour were observed––i.e. the cracks did not grow immediately upon application of the external load, but only after a certain applied stress is exceeded. The existence of such a threshold stress intensity for the onset of stable crack growth can be described by a disbalance of the residual stress intensity at the indentation crack tip and the fracture toughness after completion of the indentation cycle. A fracture mechanical description of this phenomenon is presented. The consequences which arise for the evaluation of crack growth data are explained by means of measured crack extension curves of Knoop indentation cracks in silicon nitride.

Fracture resistance behavior of alumina–zirconia composites

R-curve behavior has been examined in alumina–zirconia composites Al2O3–10wt.% ZrO2 containing two types of ZrO2 particles: 3mol% yttria doped ZrO2 and pure ZrO2. For comparison alumina ceramics was tested too. The R-curve behavior has been evaluated using two techniques for the different crack-length regimes: a small-crack R-curve by means of indentation-induced controlled Vickers crack growth in bending (ICVC) and pronounced long-crack using load-relaxation technique. The latter technique bases on the three-point bending (3PB) of the single edge notched beam (SENB). A combination of in situ microscopic crack growth observation and mechanical testing enabled measurement of crack growth resistance curves. These observations reveal the existence of increasing R-curve at the long-through thickness cracks method for tested composites. In view of contributions of residual indentation stress intensity and applied bending stress intensity, the residual stress factor χ and the fracture toughness behavior KR have been determined. SEM micrographs of typical crack profiles in tested ceramic composites were observed. Indentation strength in bending method (ISB) was used for determination fracture toughness as well.

Prediction of Fatigue Crack Growth After Single Overload in an Aluminum Alloy

An analytical method using crack driving force parameter ∆K ∗ was developed to account for the single overload interaction effects on the constant amplitude fatigue crack growth behavior in D16 (2024-T3 equivalent) aluminum alloy. Crack growth acceleration and retardation were accounted for by using residual stress intensity concept. Fatigue crack growth behavior was predicted using this method for a thin SE(T) specimen subjected to 1) constant amplitude load and 2) constant amplitude load interspersed with single tensile overloads at certain intervals of crack length. Fatigue crack growth tests were performed with these load sequences, and the experimental crack growth results obtained were compared with predictions made by use of the proposed analytical method. All of the fatigue crack growth tests were performed in a servohydraulic test machine. Crack length was measured by the traveling microscope/cellulose acetate replication method. A fairly good correlation was obtained between the experimental and predicted fatigue crack growth curves under the applied loading sequence.

Fatigue crack growth in random residual stresses

This paper deals with the effect of random residual stresses on fatigue crack growth. First, we propose a probabilistic model for residual stresses and then we show how the basic statistical information on the residual stress distribution can be included into the evaluation of the residual stress intensity factor Kr(a) and then into the crack growth equations as well as in the life-time assessment. The general analysis is illustrated explicitly for some selected specific examples.

A threshold stress intensity factor at the onset of stable crack extension of Knoop indentation cracks

Observation of the stable growth of indentation cracks in controlled bending tests is an attractive tool to study the R-curve behaviour of ceramic materials. In some crack growth experiments deviations from the ideal behaviour were observed––i.e. the cracks did not grow immediately upon application of the external load, but only after a certain applied stress is exceeded. The existence of such a threshold stress intensity for the onset of stable crack growth can be described by a disbalance of the residual stress intensity at the indentation crack tip and the fracture toughness after completion of the indentation cycle. A fracture mechanical description of this phenomenon is presented. The consequences which arise for the evaluation of crack growth data are explained by means of measured crack extension curves of Knoop indentation cracks in silicon nitride.

Residual stress effects on near-threshold fatigue crack growth in friction stir welds in aerospace alloys

Friction stir welding (FSW) is being explored as a potential tool for manufacturing aluminum aerospace structures. Several joint configurations, butt, lap and fillet joints have been made in the production of such exploratory structures. Research work on S–N fatigue and fatigue crack growth in the weld zone is required to provide an understanding and tools to assess the damage tolerance issues in friction stir welded joints and structures. In this work, results of a study conducted on near-threshold fatigue crack growth in friction stir welded aluminum alloy 7050-T7451 and a titanium alloy Ti–6Al–4V are presented. Tests were conducted on weld coupons as a function of specimen geometry (compact tension, eccentrically loaded single edge and center-crack tension) and stress ratio to understand the effects of residual stresses in the heat affected zone (HAZ) of the alloy. Residual stresses were measured on samples machined from the friction stir welded plates prior to testing. The crack growth results show that residual stresses play a key role in the crack growth parallel to the weld-path in the HAZ. Although friction stir welding process induced low residual stresses in the welds, they are found to produce large effects on the near-threshold fatigue crack growth. In general, the magnitude of the shift in the fatigue threshold in the friction stir welded coupons is a function of microstructure, residual stresses and specimen geometry. However, for a constant microstructure, fatigue thresholds at low stress ratios, were specimen geometry dependent. The thresholds were either higher or lower than those of the parent material. At high stress ratio, the differences due to the specimen geometry vanish. Stress ratio studies show that the center-crack tension geometry is less sensitive to the residual stress effects compared to the compact tension geometry. Crack growth analysis using equivalent residual stresses was used to determine the residual stress intensity factor and predict stress ratio effects. The role of microstructure on the fatigue threshold in the welds is also discussed.

OS4(3)-11(OS04W0298) Evaluation of Residual Stress Distributions and Stress Intensity Factors Based on Crack Opening Displacement Distribution Measured Along Crack in a Finite Plate

OS4(3)-11(OS04W0298) Evaluation of Residual Stress Distributions and Stress Intensity Factors Based on Crack Opening Displacement Distribution Measured Along Crack in a Finite Plate

OS04W0298 Evaluation of residual stress distributions and stress intensity factors based on crack opening displacement distribution measured along crack in a finite plate

OS04W0298 Evaluation of residual stress distributions and stress intensity factors based on crack opening displacement distribution measured along crack in a finite plate

An Elastic-Plastic Stress Analysis in a Thermoplastic Composite Cantilever Beam Loaded Uniformly

In this study an elastic-plastic stress analysis is carried out on a steel fiber reinforced thermoplastic composite cantilever beam loaded uniformly at the upper surface. An analytical solution is found satisfying both the governing differential equation in two dimensional case and boundary conditions. In this solution, the intensity of the uniform force is chosen small, therefore the transversely normal stress component is neglected in comparison with the other stress components. The thermoplastic matrix is reinforced unidirectionally by steel fibers. The orientation angles of the fibers are chosen as 0°, 30°, 45°, 60° and 90°. The plastic region begins first at the upper surface of the beam for 30° and 45° orientation angles. However, it starts earlier at the lower surface for 60° orientation angle. The intensity of the normal residual stress component in the axial direction of the beam is maximum at the upper and/or lower surfaces in the beam. The intensity of the shear residual stress is maximum on or around the axial axis of the beam.

A Study on the Influence of Mechanical Properties on the Distribution of Axial Residual Stress after Cold Drawing of Metallic Bars

Investigation was carried out on the influence of mechanical properties on the intensity of axial residual stress after cold drawing of metallic bars. Yield stress, Young's modulus, and work-hardening ratio were chosen as indications of mechanical properties, and quantitative influence was examined numerically on an ordinary cold drawing. After examining the quantitative influence of mechanical properties on the axial residual stress after drawing, further numerical experiments were carried out on the skin-pass effect in reducing the intensity of axial residual stress distribution, which the authors presented a result in the previous study by using S45C steel bars. In order to clarify the validity of the numerical analysis, various materials of different mechanical properties were selected, and cold drawing experiments were carried out in a laboratory to check the validity of the numerical results. The materials selected were (1) high-carbon steel, (2) medium carbon steel, (3) copper, and (4) aluminum. The residual stress was measured by Sachs method, and good agreement was obtained between the calculated and measured results in any case. It was found that the axial residual stress distribution is most sensitive to the work-hardening ratio, and an optimum skin-pass drawing condition was presented by quantitatively examining the effect of skin-pass in reducing the axial residual distribution.

Foreign object damage and fatigue crack threshold: Cracking outside shallow indents

Foreign Object Damage (FOD) usually happens when objects are ingested into jet engines powering military or civil aircraft. Under extreme conditions, FOD can lead to severe structural damage. More commonly it produces local impacted sites of the fan and compressor airfoils, lowering fatigue life of these components. FOD is a prime cause for maintenance and repair in aircraft engines. In this paper, a framework for analyzing FOD and its effect on fatigue cracking is established. A finite element analysis is used to identify three relevant regimes of FOD related to the depth of penetration into the substrate, and to determine the residual stresses. Most of the emphasis in this paper focuses on fatigue cracks emerging from shallow indentations, which are generally expected to be of most practical concern. Full three-dimensional finite element solutions are obtained for semi-circular surface cracks emerging from specific locations at the indentation revealing the influence of the residual stress on the stress intensity factor distribution. For shallow indents, a relatively simple dimensionless formula for the relation between the residual stress intensity factor, the crack size, and the indentation width are developed. These results, together with results for the intensity factor variations due to cyclic loading, have been used to address the question: To what extent do the residual stresses caused by the FOD reduce the critical crack size associated with threshold fatigue crack growth? Formulas for the critical crack size are obtained. Specific results are presented for the blade alloy, Ti-6Al-4V, revealing that FOD can reduce the critical crack size by as much as 60%.

Fatigue behaviour of mullite studied by the indentation flexure method

A systematic study has been performed of the use of the Indentation Flexure Fatigue (IFF) method to study crack growth in mullite at room temperature and high temperature (1300°C). The results obtained for a mullite have been compared with previous data generated on the same material, but using the more direct compact tension method. The material produces transgranular crack growth and consequently does not show R-curve behaviour, which considerably simplifies the comparison of the data generated by both methods. The IFF method can significantly overestimate the crack tip stress intensity factor because of the way in which the residual stress intensity produced by the indentation is estimated. The experimental details that influence the test results were investigated.