Preliminarni Rezultati Vezani Za Članak

NUMERICAL DETERMINATION OF STRESS CONCENTRATION AND MATERIAL YIELDING FACTORS FOR WELDED JOINTS

Dražan Kozak

Željko Ivandić

Mr.sc. D. Kozak, University of Osijek, SF, Trg I. B. Mažuranić 18, HR-35000 Slav. Brod

Mr.sc. Ž. Ivandić, University of Osijek, SF, Trg I. B. Mažuranić 18, HR-35000 Slav. Brod

Keywords:welded joints, stress concentration factor, factor of material yielding, finite element method, stress distribution

ABSTRACT

Stress concentration factors and factor of material yielding determination for characteristic welded component applied in shipbuilding is described.Optimal shape of hot spotsdue to stress distribution by finite element analysis was analysed. Spreading of yielding zones by changing both nominal stress and radius of roundness has been presented. It is evident that factor of material yielding for nominal stress greater than one half of yield strength becomes constant.

1. INTRODUCTION

Stress gradient in the presence of sharp corners, holes, notches etc. is significant by a lot of engineering structures. Neuber's solution for the stress concentrations of notches, applying theory of elasticity, fifty years ago may be taken as beginning (H. Neuber, 1958). Ratio of maximum stresses in vicinity of discontinuity to remote applied uniaxial stress is known as stress concentration factor. Its value may be determined analytically, numerically or experimentally. Today, in most cases for solving of stress concentration effects, finite element packages should be used. Of course, the calculation of stress concentration factor is supposing linear-elastic material of structure.

However, most engineering materials are showing elastic-plastic behaviour. In this case, more sense to be applied has factor of material yielding. In regions of large material yielding and hardening appears stress redistribution. Exactly, stress distribution with its peak value may be used as a parameter of goodness of component shaping.

In this paper an optimal design of one characteristic corner welded shipbuilding structure has been investigated.

2. WELDED SIDE GUSSETS

Thin-walled shipbuilding structure with welded side gussets (Fig. 1) has been chosen (M. Wagner, 1999) to research the influence of size of roundness radius r where the weld joint cross into base metal (hot-spots) on the stress distribution.

Fig. 1 Thin-walled welded structure

The material of structure was the steel of higher strength GL-D36. The mechanical properties are given in the Table 1.

Table 1. Mechanical properties of GL-D36 steel

Chemical composition of this steel is given in the Table 2.

Table 2. Chemical composition of GL-D36 steel

The aim of the investigation was to evaluate the influence of the roundness radius size on the magnitude of the stress at the so-called hot spots by shipbuilding components tensile loaded.

The peak value of the hot spot stress determines directly the value of stress concentration factor k if the material model has been described as linear-elastic.

The characteristic of real elastic-plastic behaviour of material is the redistribution of stresses. Material yielding around hot spots may be got into consideration if the equivalent stress could to be determined. So, if the structures with irregular shape have been designed only in the respect to the nominal stress, neglecting stress concentration and material yielding, respectively, the failure may be probably expected (W. Fricke 1991).

3. FINITE ELEMENT MODELLING

Regarding the symmetry of the structure component, only one fourth of the specimen has been modelled with unit thickness. The yielding according to the thickness is not constrained and the plane stress assumption is more closed to the reality than the plane strain formulation. Isoparametric 8-node quadrilateral and 6-node triangular plane stress elements have been used to mesh the structure. The model has been made in so-called down-to-top technique with ANSYS 5.3 software (ANSYS 5.3, 1998). The wire model consists from 15 key-points and 17 lines. At the places where the weldment is joined to the base metal in the single point, stress concentration key-points may be defined. In this case radius of first row of elements about this key-point, crack tip singularity key, number of elements in circumferential direction and ratio of second row element size to the first row of elements must to be specified. Meshing parameters for smart sizing elements have been set. Finally, 5 areas created from selected lines have been meshed through 229 elements and 748 nodes. The mesh of model with applied boundary conditions is presented in Fig. 2.

Fig. 2 One fourth of finite element model of welded structurewith boundary conditions

The Figures 3. and 4. are depicting enlarged welded joint and the detail of the mesh around the stress concentration point. A matrix of 5 different geometries were investigated for 5 different sizes of r (from 0 to 8 mm) and for 5 different nominal stress values 0. (from 100 to 300 MPa).

4. STRESS CONCENTRATION FACTOR (SCF)

Failures such as fatigue brittle cracking and plastic deformation frequently occur at points of stress concentration. It is for this reason that stress concentration factors play an important role in design. The value of SCFs depend on the shape and dimensions of the component being designed and can be calculated using finite element methods. Stress concentrations arise from any abrupt change in the geometry of a specimen under loading. As a result, the stress distribution is not uniform throughout the cross-section.

Stress concentration factork in this example may be defined as:

(1)

where x is maximum stress appears around stress concentration point and 0 is nominal applied stress.

For linear-elastic material behaviour SCF has constant value for any nominal loading. Its value is varying only with the changing of radius of roundness. This variation is presented in the table 3:

Table 3. SCF decreasing with increasing of r

It has been reasonable to expect decreasing of stress concentration factor value with increasing of radius of roundness, what is clearer from the diagram presented on the Figure 5:

Fig. 5 SCF variation with changing of radius of roundness

5. FACTOR OF MATERIAL YIELDING (FMY)

If the failure can not be characterised as a brittle fracture, the material shows elastic-plastic behaviour with the yielding and hardening in the field of high stress concentrations. In this case, stress redistribution and stable crack propagation occur before ductile fracture. In the regions where equivalent stress overcomes the nominal stress value, the yielding of material appears. Then we may introduce the new parameter identified as a factor of material yielding Y:

(2)

The material yields in the region where Y ≥ 1 or eq, max ≥ 0. In our example, the bilinear isotropic hardening plasticity has been assumed as a material law (Re=431 MPa, E=210000 MPa, Rm=588 MPa, E'=565 MPa). As the first step, FMY has to be calculated varying applied loading with constant radius of roundness. In the table 4 are given the results for FMY with changing of 0 from 100 to 300 MPa (2/3 of yielding stress) by constant radius of 1 mm:

Table 4. Factor of material yielding Yvs. nominal stress 0(r = 1 mm)

It is evident from the table 4 that FMY decreases with applied stress 0 increasing. However, the equivalent stress value has slow growth and zones of yielding are larger with every step of load increasing, what can be seen from Figure 6.

If the similar calculations for other radiuses of roundness are repeated, it is possible to present all curves of FMY vs. nominal stress for r = 0, 1, 2, 4 and 8 mm (Fig. 7). One can conclude that curve of FMY variation is less steep for bigger radiuses of roundness. Also, after some amount of applied stress (250 MPa in analysed example), FMY becomes constant and independent of radius of roundness value. This is consequence of stress redistribution in the more large area with load increasing.

Fig. 7 Factor of material yielding vs. applied nominal stress for different r

Finally, for the maximum applied stress of 300 MPa, the equivalent stress distribution for analysed radiuses of roundness has been investigated (Figure 8).

Fig. 8 Equivalent stress distribution with increased radius of roundness

The worst situation due to stress distribution is present without performed roundness (r = 0 mm). The yielding area is large and relatively deep into material. Only 1 mm of roundness radius contributes to significant smaller yielding area. The peak of maximum stress is displaced from the edge for r = 4 mm. The stress distribution is much better. If the roundness radius is 8 mm, the yielding zone doesn’t exist. The performance of construction with r = 8 mm can achieve avoidance of any region where material yields.

6. CONCLUSIONS

Four important conclusions from performed analysis can be drawn:

-stress concentration factor value decreased with radius of roundness increasing,

-curve of material yielding factor variation is steeper for smaller radiuses of roundness,

-factor of material yielding becomes constant and independent of radius of roundness value after some amount of applied loading and

-the stress distribution is much suitable without peak values for enough large radius of roundness.

This work is financially supported by project No 152504 'Numerical modelling of mis-matching welded joints with cracks'.

7. LITERATURE

1. H. Neuber: Theory of notch stresses, Springer, Berlin, 1958.
2. M. Wagner: Schwingfestigkeit geschweißter Konstruktionsdetails, Konstruktion, Juli/August 7/8, 1999.
3. W. Fricke; S. Pohl: Ermittlung und Katalogisierung von Formzahlen für schiffbauliche Konstruktionsdetails, T.1. Hamburg: Germanischer Lloyd, 1991.
4. ANSYS 5.3, Manual Guide 1998.
5. R. E. Peterson: Stress Concentration Factors, Charts and Relations useful in Making Strength Calculations for Machine Parts and Structural Elements, John Wiley and Sons, New York, 1974.