Notch Strain Research Articles

A Yield Surface Approach to the Estimation of Notch Strains for Proportional and Nonproportional Cyclic Loading

An analytical method is developed to estimate notch root strains in a notched bar of elastic-plastic, isotropic material subjected to proportional and nonproportional multiaxial nominal loading. The method uses anisotropic plasticity theory to define a structural yield surface in nominal stress space that incorporates both the isotropic material properties and the anisotropic geometry factors of the notch. Notch root plastic strain increments and anisotropic work-hardening effects are then related to this yield surface using standard methods of plasticity. Comparisons of the proposed method with previously published strain estimates using the finite element method for a notched shaft under proportional nominal bending and torsion, and with strain gage measurements of a circumferentially notched solid steel shaft subjected to a series of box-shaped nonproportional loading paths in tension-torsion nominal stress space are presented. The strain calculations agree well both qualitatively and quantitatively using an appropriate nominal load-notch plastic strain relationship, and are suitable for strain-life fatigue calculations.

Stress and strain range predictions for axisymmetric and two-dimensional components with stress concentrations and comparisons with notch stress-strain conversion rule estimates

A comparison is made between finite element predictions of strain and strain range for hollow tubes with axially loaded axisymmetric internal projections and values obtained from the simple notch stress-strain conversin (NSSC) rules. Data from other published analyses, where notch strains were predicted, support this investigation. The comparison is made for a variety of monotonic and cyclic loads, material hardenning assumptions, and geometries. An intermediate rule ( m = 0.5) which appears to correlate with the finite element predictions to a reasonable degree of accuracy, is identified. In addition, an analytical relationship is suggested for calculating strain and strain range, in terms of load level, strain hardening assumption, and elastic stress concentration factor (SCF) for this type of axisymmetric component. Also, a comparison is made between some previously published experimental and numerical data, obtained for other two-dimensional and axisymmetric problems, and NSSC rule estimates in order to confirm the suitability of the intermediate rule. Finally, on the basis of these comparisons, an approximate procedure for predicting stress and strain ranges under conditions of gross yielding is presented for plane stress, plane strain, and axisymmetric problems.

A model for a long life fatigue behavior of small notches: Ting, C.-H. Diss Abstr Int52 11 (may 1992) 208 pp

The applicability of the notch strain approach to the assessment of the fatigue strength and service life of a K-shaped tubular joint is investigated. The structural stresses in the hot spot area are calculated by the finite element method and compared with the results of relevant parametric formulae as well as of strain gauge measurements. The stress concentration factor at the weld toe is determined on the basis of a plane cross-sectional model of the weld at the hot spot. The elastic–plastic notch strains are derived therefrom using the cyclic stress strain curve of the material (finite element results and approximations according to Neuber and Sonsino). The fatigue strength of the tubular joint under constant-amplitude loading is predicted on the basis of the strain S–N curve. The service life under variable-amplitude loading in seawater is derived using the Miner rule. The notch strain approach for welded joints results in unacceptably large differences in the predicted strength and life values under similarly acceptable assumptions in respect of material state, local hardness and residual stress. The inhomogeneity of material and hardness at the weld toe seems to be the main reason for the discrepancies.

Notch strain calculations for axisymmetric problems based on a local strain approach

Notch strain calculations for axisymmetric problems based on a local strain approach

MEAN STRESS EFFECTS ON LOW CYCLE FATIGUE FOR A HIGH STRENGTH STEEL

Abstract— ASTM A723 Q & T steel with a yield strength and ultimate strength of 1170 and 1262 MPa respectively was evaluated for mean stress‐strain effects under smooth specimen axial strain controlled low cycle fatigue conditions with strain ratios R of −2, −1, 0, 0.5 and 0.75. Cycles to failure ranged from 15 to 105. Cyclic stress‐strain response based upon half‐life hysteresis loop peaks were similar for all R ratios. Mean stress relaxation occurred for R≠−1 only when plastic strain amplitudes were present and this occurred above total strain amplitudes of 0.005. Thus, mean stress relaxation was completely dependent upon cyclic plasticity. Mean strains did not affect low cycle fatigue life unless accompanied by half‐life mean stress. Tensile mean stress was detrimental and compressive mean stress was beneficial and these effects only occurred at strain ampltidues below 0.005. Three different mean stress models were used to evaluate the low cycle fatigue data and the SWT log‐log linear model best represented the data. These results can be used with the local notch strain fatigue life prediction methodology.

Quantifying design rationale for vehicle structures st Ponsford, A.Automot. Eng. (UK) Feb-Mar. 1990 15, (1), 26–29

The applicability of the notch strain approach to the assessment of the fatigue strength and service life of a K-shaped tubular joint is investigated. The structural stresses in the hot spot area are calculated by the finite element method and compared with the results of relevant parametric formulae as well as of strain gauge measurements. The stress concentration factor at the weld toe is determined on the basis of a plane cross-sectional model of the weld at the hot spot. The elastic–plastic notch strains are derived therefrom using the cyclic stress strain curve of the material (finite element results and approximations according to Neuber and Sonsino). The fatigue strength of the tubular joint under constant-amplitude loading is predicted on the basis of the strain S–N curve. The service life under variable-amplitude loading in seawater is derived using the Miner rule. The notch strain approach for welded joints results in unacceptably large differences in the predicted strength and life values under similarly acceptable assumptions in respect of material state, local hardness and residual stress. The inhomogeneity of material and hardness at the weld toe seems to be the main reason for the discrepancies.

On an unified model for predicting notch strength and fracture toughness of metals

In the present paper an unified model for predicting the notch strength and the fracture toughness, K IC , is given and checked on the basis of summarizing the recent research. The crack initiation at notch tip may be assumed to occur due to the fracture of the hypothetical material element located at notch root. Hence the crack initiation criterions are developed from the notch strain analysis and the well-known fracture criterions for various kinds of metals. If the fracture of the notched element occurs right after the crack initiation at notch tip without any subcritical crack propagation, the notch strength, i.e. the fracture stress of the notched element will be equal to the stress for crack initiation at notch tip. As a result, the formulae for predicting the notch strength from tensile properties are obtained for various kinds of metals. The formula for predicting the apparent fracture toughness, K 1A , can be also given in the same way. The predicted notch strength of metals agree well with the test results in literature. However, it should be pointed out that the predicted notch strength in plane stress state is the lower limit of the test results. More important may be that a new material constant, the so-called nonsensitivity-to-notch factor, is introduced to evaluate the notch sensitivity, or the notch toughness of metals. It has been pointed out that the crack must be bluntened during loading in order to keep the mechanical equilibrium at crack tip and the radius of the bluntened crack tip must have a critical value. Taking the bluntened crack as a sharp notch and ρ c as the critical radius of the bluntened crack tip, the formula for predicitng the fracture toughness, K IC , from tensile properties is obtained for the ductile metals, based the assumption mentioned above. For the steels with lath Martensite microstructure, ρ c will be equal to the strain hardening exponent in mm, and for steels with mixed Martensite structure ρ c is equal to the uniform elongation in mm, or the Austenite grain size, or 9 times of the dimple size. The difference between the predicted values of K IC and the test results are mostly less than 10. The values of K IC of aluminium alloys can be also predicted by a modified formula and the tensile properties.

Use of Neuber's rule to estimate the fatigue life of notched specimens of ASME SA 106-B steel piping in 288°C air

Fatigue strain-life tests were conducted on notched specimens of ASME SA 106-B piping steel at PWR operating temperatures (288°C (550°F)), under completely reversed loading. Fatigue limits at 10 7 cycles were estimated for smooth specimens to be 185 MPa (26·8 ksi) at 24°C and 232 MPa (33·7 ksi) at 288°C. The higher fatigue strength observed at the PWR temperature is postulated to be caused by dynamic strain aging processes. However, a reduction in fatigue strength in the low cycle fatigue regime was observed in 288°C air environment tests, which may indicate that the current ASME Section III design curve for carbon steels is nonconservative in its positioning. Notch strain histories were estimated for the notched specimen tests using various interpretations of Neuber's rule. It was concluded that the use of the fatigue notch concentration factor (K f) in the Neuber relation in conjunction with the uniaxial cyclic stress-strain curve provided the best correlation of notched specimen fatigue data with results obtained from smooth sp̀ecimen tests. The notched specimen strain-life results derived from the application of Neuber's rule alone proved to be conservative when compared with smooth specimen test results to such an extent that Neuber-generated notch stresses and strain amplitudes cannot accurately be compared with the mean data curves derived from the ASME Section III fatigue curves for carbon steels which are based on net section stress measurements.

Fatigue Life Estimates for a Notched Member in a Corrosive Environment

It is often assumed that the effects of an aggressive environment can be included in fatigue life estimation procedures by determining the material properties in the environment and at the frequency of interest. An analytical and experimental program was conducted to confirm or refute this assumption. Automotive grade aluminum alloy, 5454-H32, in 3 percent NaCl solution and laboratory environment was selected for this study. A simple model where the total fatigue life is the summation of the portion where fatigue damage is best described by the notch strain field, and the portion where nominal stress and crack length dominate damage assessment, was used to estimate fatigue lives for center notched plates. Smooth cylindrical specimens were employed to determine the material properties for initiation. The environment had a large influence on the initiation resistance of this material at long fatigue lives, whereas at shorter fatigue lives (i.e., <104 cycles) there was little effect. Center cracked plates were used to determine the crack growth rates. Linear elastic fracture mechanics concepts were employed to estimate crack propagation lives. Approximately a factor of three reduction in crack propagation life was attributable to the hostile environment. Center notched plate specimens with Kt = 2.4 and Kt=5.1 were tested in both environments to examine the model. The accuracy of the fatigue life predictions in relation to the experimental data were comparable in 3 percent NaCl solution to the results obtained in laboratory air.

Energy density approach to calculation of inelastic strain-stress near notches and cracks

An energy-based method of calculating elastic-plastic strains and stresses near notches and cracks is presented. It was assumed that the strain energy density in the plastic zone ahead of a notch can be calculated on the basis of the elastic stress-strain solution. Good agreement between the calculated and measured notch strains was obtained for several notches, materials and loading conditions. It was shown that the assumption holds up to general plastic yielding. This method can also be applied in uniaxial and multiaxial stress states. A numerical procedure suitable for any material stress-strain curve is presented. Some possibilities concerning elastic-plastic stress-strain calculation near cracks are also discussed.

Simple Methods of Estimating the Stress and Strain at the Notch Root

An elastic-plastic analysis of notched plates subjected to tension force or bending moment was made. Based on this analysis, methods of evaluating approximately the stress and strain at the notch root were proposed. Dimensionless master curves were proposed for estimating the stress and strain concentration factors under small-scale yielding condition and the stress and strain at the notch root under large-scale yielding condition. This master-curve approach was found valid in all the cases analysed in this study. A simple formula was further developed by which the stress and strain at the notch root could approximately be calculated under load conditions below and above the gross yield stress by using the J-integral, together with a formula for estimating the J-integral. The estimated values of the notch stress and strain by this set of the approximation formulae agreed well with the results of numerical analysis.

Fatigue life prediction of notched members based on local strain and elastic-plastic fracture mechanics concepts

Fatigue life predictions for notched members are made using local strain and elastic-plastic fracture mechanics concepts. Crack growth from notches is characterized by J-integral estimates made for short and long cracks. The local notch strain field is determined by notch geometry, applied stress level and material properties. Crack initiation is defined as a crack of the same size as the local notch strain field. Crack initiation life is obtained from smooth specimens as the life to initiate a crack equal to the size of cracks in the notched member. Notch plasticity effects are included in analyzing the crack propagation phase. Crack propagation life is determined by integrating the equation that relates crack growth rate to ΔJ from the initiated to final crack size. Total fatigue life estimates are made by combining crack initiation and crack propagation phases. These agree within a factor of 1.5 with measured lives for the two notch geometries.

Elastic-Plastic Analysis of Blunt Notched CT Specimens and Applications

An elastic-plastic plane strain analysis of blunt notched compact tension specimens used in fatigue crack initiation tests is presented. Using this analysis it is shown that under conditions of constrained plastic flow in the notch region, the functional relationship between total notch strain and an elastically calculated notch stress is nearly the same for different notch sharpnesses. This material dependent functional relation is shown to hold for some other geometric stress concentrations as well. Under conditions where this relationship is the same it should be possible to correlate fatigue crack initiation data by means of the elastically calculated notch stress.

Some Studies of the Influence of Localized and Gross Plasticity on the Monotonic and Cyclic Concentration Factors

Abstract The variation in monotonic and cyclic concentration factors (namely, Kt, Kε, Kσ) due to localized and gross plasticity is presented and discussed for two alloys of contrasting stress-strain behavior, an aluminum alloy 2024 T351 and a mild steel SAE 1015. Thin plates with circular and elliptical holes made of these alloys were subjected to monotonic and cyclic straining in a servo controlled testing machine. Predominant in the monotonic behavior of the concentration factors is the rapid increase in strain concentration factor in notched mild steel plates, attributed to the unrestrained plastic flow (Lüders deformation) characteristic of this material. Such behavior is compared to the response of the continuously strain hardening aluminum alloy when subjected to a similar nominal strain history. The dominant feature of the cyclic behavior is the variation in the notch strains as influenced by the overall hardening or softening phenomenon which accompanies cyclic plastic deformation. With the aid of these results, the accuracy of the Neuber rule is checked and restrictions to its application in fatigue life predictions of notched members using smooth specimen data are presented.

Elastic-Plastic Deformation in Edge-Notched Tension Specimens Under Plane Stress Conditions

An elastic-plastic, plane stress, finite element analysis has been performed on edge-notched tension members having elastic stress concentration factors of 2.28 and 3.06. For net section stresses below general yield, experimentally measured notch root strains are within 12 percent of those computed by the finite element method. The current results indicate that finite element analysis generally provides a better estimate of notch strain than either the Neuber or Hardrath-Ohman formulations.