Microstructural Support Length Research Articles

Fatigue assessment of welded joints at sub-zero temperatures by means of stress averaging approach

ABSTRACT The problem of typical stress-based fatigue assessment methods is that additional influencing factors like temperature effects do not directly influence the respective stress and can thus only be incorporated via modification factors. The stress averaging approach is expected to account for effects that influence the support around notches via the micro-structural support length ρ*. This study thus investigates the applicability of the stress averaging approach for welded joints in engineering structures exposed to sub-zero temperatures. For this purpose, fatigue test results of welded joints in the temperature range of 20°C down to −50°C are assessed. It is shown that it is possible to assess data for different temperature with the same reference fatigue curve while maintaining a small scatter without the need for modification factors.

Neuber fictitious notch rounding approach reformulated for orthotropic materials

In this short contribution, the fictitious notch rounding concept is applied to U-shaped notches in orthotropic bodies. Using the normal stress criterion, the fictitious notch radius is determined in closed form. It is found that the fictitious radius strictly depends on the actual notch radius, the microstructural support length and the elastic properties of the material, the latter playing a crucial role.

V-notch tip subjected to in-plane mixed mode loading: overview of recent results and possible future outcomes

The fictitious notch rounding concept is applied for the first time to V-notches with root hole subjected to in-plane mixed mode loading. Outof- bisector crack propagation is taken into account. The fictitious notch radius is determined as a function of the real notch radius, the microstructural support length and the notch opening angle. Due to the complexity of the problem, a method based on the simple normal stress failure criterion has been used. It is combined with the maximum tangential stress criterion to determine the crack propagation angle. An analytical method based on Neuber's procedure has been developed. The method provides the values of the microstructural support factor as a function of the mode ratio and the notch opening angle. The support factor is considered to be independent of the microstructural support length. Finally, for comparison, the support factor is determined on a purely numerical basis by iterative analysis of FE models.

A review of the notch rounding approach under in plane mixed mode loading

The fictitious notch rounding approach is widely used for the fatigue assessment of welded joints and for this reason in the present paper a review of the concept applied to inclined lateral V-notches with root hole subjected to in-plane mixed mode loading has been carried out. This is the basis for future applications to welded structures in presence of mixed mode loading.The analytical framework of the method is herein recalled and the fictitious notch radius is determined as a function of the real notch radius, the microstructural support length and the notch opening angle. In order to reduce the complexity of the task, we adopt a method based on the normal stress failure criterion. The method provides the values of the microstructural support factor as a function of the mode mixity parameter and the notch-opening angle. Moreover, the support factor is assumed independent of the microstructural support length. Finite element simulations for various notch shape and configurations are compared to experimental data from pointed V-notches made of polymethylmethacrylate. The model prediction showed good agreement with the experimental results. These results are very promising for the application to welded structures.

Tilted lateral V-notches with root hole subjected to in-plane mixed mode loading: Fictitious notch rounding concept

The fictitious notch rounding concept is applied for the first time to inclined lateral V-notches with root hole subjected to in-plane mixed mode loading. Out-of-bisector crack propagation is taken into account by combining the fictitious notch rounding approach with the maximum tangential stress criterion. Following the guidelines of a previous paper dealing with internal notches, the fictitious notch radius is determined as a function of the real notch radius, the microstructural support length and the notch opening angle. The problem is of formidable complexity and for this reason a simple method based on the normal stress failure criterion is adopted here. The analytical method based on Neuber's procedure proposed for central notches is extended here to tilted lateral notches. The method provides the values of the microstructural support factor as a function of the mode mixity parameter and the notch opening angle. The support factor is considered to be independent of the microstructural support length. To validate the approach about two thousands finite element analyses have been performed varying the notch shape and load configuration. Finally an experimental validation has been performed considering a complete set of data from pointed V-notches made of polymethylmethacrylate.

Crack Initiation at V-Notch Tip under In-Plane Mixed Mode Loading: A Review of the Fictitious Notch Rounding Concept

The fictitious notch rounding concept has been recently applied for the first time to V-notches with root hole subjected to in-plane mixed mode loading. Out-of-bisector crack propagation is taken into account. The fictitious notch radius is determined as a function of the real notch radius (the microstructural support length) and the notch opening angle. Due to the complexity of the problem, a method based on the simple normal stress failure criterion has been used. It is combined with the maximum tangential stress criterion to determine the crack propagation angle. An analytical method based on Neuber’s procedure has been developed. The method provides the values of the microstructural support factor as a function of the mode ratio and the notch opening angle. The support factor is considered to be independent of the microstructural support length. Finally, for comparison, the support factor is determined on a purely numerical basis by iterative analysis of finite element models. The present paper is aimed to give a brief overview of the recent findings on this challenging topic making clear the state of the art.

Crack initiation at V-notch tip subjected to in-plane mixed mode loading: An application of the fictitious notch rounding concept

The fictitious notch rounding concept is applied for the first time to V-notches with root hole subjected to in-plane mixed mode loading. Out-of-bisector crack propagation is taken into account. The fictitious notch radius is determined as a function of the real notch radius?? the microstructural support length and the notch opening angle. Due to the complexity of the problem, a method based on the simple normal stress failure criterion has been used. It is combined with the maximum tangential stress criterion to determine the crack propagation angle. An analytical method based on Neuber's procedure has been developed. The method provides the values of the microstructural support factor as a function of the mode ratio and the notch opening angle. The support factor is considered to be independent of the microstructural support length. Finally, for comparison, the support factor is determined on a purely numerical basis by iterative analysis of FE models.

V-notches subjected to combined tension and torsion loadings: the application of the fictitious notch rounding concept

The fictitious notch rounding concept is applied for the first time to V-notches subjected to combined modes I and III loading. The fictitious notch radius is determined as a function of the real notch radius, the microstructural support length and the notch opening angle. Due to the complexity of the problem, a method based on the simple normal stress failure criterion has been employed in the present contribution. An analytical method based on the original Neuber’s procedure has been developed. The method provides the values of the microstructural support factor as a function of the mode mixity ratio and the notch opening angle. The support factor is considered to be independent of the microstructural support length. The determined support factors are validated by means of a purely numerical basis by means of a large bulk of FE models. Finally the criterion is applied to a set of data taken from the literature.

Fictitious notch rounding concept applied to V-notches with root hole subjected to in-plane mixed mode loading

The fictitious notch rounding concept is applied for the first time to V-notches with root hole subjected to in-plane mixed mode loading. Out-of-bisector crack propagation is taken into account. The fictitious notch radius is determined as a function of the real notch radius, the microstructural support length and the notch opening angle. Due to the complexity of the problem, a method based on the simple normal stress failure criterion has been used. It is combined with the maximum tangential stress criterion to determine the crack propagation angle. An analytical method based on Neuber’s procedure has been developed. The method provides the values of the microstructural support factor as a function of the mode ratio and the notch opening angle. The support factor is considered to be independent of the microstructural support length. Finally, for comparison, the support factor is determined on a purely numerical basis by iterative analysis of FE models.

The fictitious notch rounding approach applied to V-notches with root holes subjected to mode I loading

The fictitious notch rounding concept is applied here to V-shaped notches with root holes subjected to mode I loading. The fictitious notch radius ρf is determined as a function of the real notch radius ρ, the microstructural support length ρ* and the notch opening angle 2α, at first using the normal stress criterion. Two analytical methods have been developed resulting in closed-form expressions for the multiaxiality factor s in the well-known relationship ρf = ρ + sρ*. The first method expresses the notch stress averaged over the microstructural support length at pointed V-notches by the maximum notch stress of fictitiously rounded V-notches (with root hole), taking advantage of a newly developed analytical solution. The second method considers V-notches with root holes both in the real and in the fictitious configuration. It uses a procedure given by Neuber. Finally, different failure criteria are considered using the first method. Plane stress and plane strain conditions, respectively, are evaluated.

Fictitious notch rounding concept applied to V-notches with root holes subjected to in-plane shear loading

The fictitious notch rounding concept is applied here for the first time to V-shaped notches with root hole subjected to in-plane shear loading. The fictitious notch radius is determined as a function of the real notch radius, the microstructural support length and the notch opening angle, at first using the normal stress criterion in combination with the maximum tangential stress criterion for finding the crack propagation angle. Two analytical methods have been developed resulting in closed form expressions for the multiaxiality factor s. Finally, for comparison, the factor s is determined also on a purely numerical basis by iteration of FE-models.

A Comprehensive Numerical Stress—Strain Analysis of Laser Beam Butt-Welded Titanium Compared with Austenitic Steel Joints

Experimental tests on laser beam butt-welded joints made of commercially pure titanium and Ti—6Al—4V alloy showed a fatigue behaviour quite different from that usually observed in the case of AISI 304 joints connected with the same welding technique. In fact, fatigue failures of titanium joints were observed at the level of the base material but not in the notch region, as have been found for austenitic steel. In order to explain this experimental evidence, very detailed finite element models are developed in this paper. The models reproduce the real cord profiles of Ti—6Al—4V and AISI 304 steel welded joints detected by a high-precision coordinate measuring machine. Furthermore, mechanical properties given as input to the finite element models correspond to the real joint microstructure revealed by micro-hardness tests carried out in the different regions of the specimen. Finally, finite element models reproduce the distribution of porosity detected via microscopic inspection of the fractured surfaces. Interactions of weld geometry, material properties, presence/absence of porosity, and level of applied stress are considered in this study, which includes nine different finite element models of titanium and austenitic steel joints. A relevant complication in the analysis of titanium joints is represented by the small thickness and stress concentration effects. Numerical results show that the stress field in titanium joints is sensitive to the combined effect of weld seam geometry and presence of welding defects (pores). The latter produces stress concentration much more severe than that caused by the weld cord. Microstructural support length evaluated near the pores of titanium joints is about the same as that computed near the notch of austenitic steel joints (i.e. near 0). Furthermore, the Topper parameter evaluated for the titanium joints in the presence of pores is much smaller than for the stainless steel joints. Microstructure modifications must be accounted for in order to assess correctly the fatigue behaviour of austenitic steel joints.

Fatigue‐relevant stress field parameters of welded lap joints: pointed slit tip compared with keyhole notch

ABSTRACTThe notch stress intensity factor (NSIF) based analytical frame is applied to the slit tips (or weld roots) of welded joints with inclusion of the T‐stress component. This T‐stress can be determined from FE models evaluating the ligament stresses close to the pointed slit tip. An alternative analytical frame is presented for the corresponding keyhole notches based on analytical solutions from the literature, which are applied to the ligament stresses.In the slit tip models, the mean local strain energy density (SED) with inclusion of the T‐stress effect is determined analytically and numerically in comparison, using two different fatigue‐relevant control radii, R0= 0.28 mm and R0= 0.15 mm, the former value well proven for thick‐sheet welded joints made of structural steel. The latter smaller value is tentatively proposed for thin‐sheet welded joints, in the direction suggested in the recent literature where a reduction of the microstructural support length for laser beam welds and resistance spot welds is recommended. The FEM‐based and analytical stress concentration factors (SCF) for the lap joint keyhole model and also the SED values for the corresponding pointed slit tips are found to be in good agreement. The J‐integral consisting of the first and second component (the latter containing the T‐stress) is compared with the corresponding SED values.

Fictitious notch rounding concept applied to sharp V-notches: Evaluation of the microstructural support factor for different failure hypotheses: Part II: Microstructural support analysis

On the basis of the comprehensive and accurate stress field equations for sharp rounded V-notches derived in Part I of this contribution, the microstructural support factor of these notches is determined which quantifies the fictitious notch radius in Neuber’s elastic microstructural support concept. By means of Filippi’s equations and considering different failure criteria (Rankine, von Mises and Beltrami) the fictitious notch radius is evaluated for different notch opening angles as a function of the actual notch radius and the microstructural support length. Plane stress and, alternatively, plane strain conditions are introduced. Once the fictitious radius has been found, the support factor s is derived from the expression: fictitious notch radius minus actual notch radius divided by microstructural support length. The support factor s is found to be very sensitive to the notch opening angle, but constant ‘plateau values’ are determined for an actual radius greater than the microstructural support length. The dependence of s on the failure criterion and the multiaxiality conditions (plane stress or plane strain) is also investigated. Various numerical analyses using the FE method have been carried out to compare the theoretical stress concentration factor to the effective stress concentration factor, the former obtained by considering fictitiously rounded notches under tension loading using the plateau values of s, the latter obtained by integrating the relevant stress over the microstructural support length along the bisector of the pointed V-notch. Finally, dealing with out-of-plane shear loading, Neuber’s corresponding solution valid for sharp rounded notches is re-evaluated and the numerical analysis described above is extended to this loading case. All the comparisons above are preceded by elementary solutions for pointed notches in general. It is shown that the plateau values of s are well suited for engineering usage in structural strength assessments.

Relationships between J-integral and the strain energy evaluated in a finite volume surrounding the tip of sharp and blunt V-notches

The concept of “elementary” volume and “micro structural support length” was introduced many years ago by Neuber. Neuber formulated the idea that, also in the presence of a sharp notch, a generic material is sensitive to a fictitious root radius whose value is only simply correlated to the ‘micro-structural support length’ and to the multiaxiality of the stress state. On the other hand, Rice’s J-integral is a commonly used elastic and elastic-plastic fracture parameter for the description of the local fields in the neighbourhood of stress concentrations and for the study of crack initiation and propagation. In order to be applied to un-cracked geometries, J-integral needs a path definition. A particular control area, which embraces the tip of sharp and blunt notches, is defined here, and over that area the mean value of the strain energy E (e) and J-integral are determined under Mode I loading. The semi-moon-like area Ω adapts itself as a function of the notch geometry leaving unchanged its depth R c measured on the notch bisector line. The variability of the E (e)/ J ratio versus R c is analysed considering sharp V-notches as well as blunt notches with a semicircular root and an opening angle ranging from 0° to 135°. The analyses demonstrated that a linear law permits a link between the two parameters in the case of sharp V-notches and blunt V-notches with a large opening angle. By decreasing the angle, the linear law is valid only as a first approximation, due to the increasing influence of two elliptic integrals in the analytical formulation of J. Some elastic-plastic analyses limited to V-notches with a large opening angle confirm those findings.