Notch Effect on Brittle-Ductile Transition Behaviour of Construcytion Steel

Grain size effect on brittle-ductile transition behaviour of mild steel

S. Dadvandipour, L. Tóth

Bay Zoltán Institute of Logistics and Production Engineering

3519 Miskolc- Tapolca, Iglói u.2.

Hungary

E-mail:

Abstract

The brittle-ductile transition behaviour of mild steel with different grain size is discussed by introducing the notch stress, notch strain and notch energy intensity concept. This concept includes the maximum local elasto-plastic strain , stress energy at the notch vicinity and their distribution. The validity of this concept is proved by the well-known fact that by increasing the grain size the brittle-ductile sesitivity also increases.

Keywords: Brittle-ductile behaviour , mild steel, notch sensitivity, notch stress intensity factor , notch strain intensity factor, grain size and local parameters.

1. Introduction

The reliability and life time of engineering structures are determined by the external and internal local stress, strain concentrators. The internal stress, strain concentrators are caused by microstructure inhomogenities of materials, the external ones by notches. It is obvious that it is not possible to design a construction without considering the effects of stress, strain concentrators. The behaviour of local areas at notches is determined by the notch geometry, loading conditions and the local material responses. From the engineering point of view the so called "notch effect" is very important, first in brittle-transition behaviour and second in fatigue failure of structural elements.

either totally ductile or brittle or brittle-ductile characters.It is clear that the ratio of ductile and brittle areas depends on factors influenced by the notch geometry, testing conditions and material behaviour. These fracture surfaces are schematically illustrated in Fig. 1. From microscopic point of view we can find a ductile fracture surface at the notch vicinity even at the most dangerous loading conditions (i.e. at high loading rate, and at low temperatures) . This phenomena can be realised at the notches with a highest notch acquity (i.e. in the case of crack). Obviously these areas could have only a magnitude of grain size. Considering only the macroscopic approach the following question can arise: How is the brittle-ductile behaviour of materials of notched elements described and how can the effect of loading conditions (temperature and loading rate) and the notch geometry be taken into account?

This paper deals with brittle-ductile behaviour of notched tensile specimens on the basis of notch stress, strain and energy intensity concept proposed by one of the authors of this paper [1,2,3]. The validity of this approach is controlled by tensile test on notched specimens made of mild steel with different grain size and tested at -196C.

1.1. Notch stress, strain and energy intensity concept

The notched specimens under tensile test may have different fracture surfaces. From macroscopic point of view they are

Fig. 1. The possible fracture surfaces of notched specimens tested in tensile. The ductile, brittle or ductile-brittle transition behaviour of stress concentrators depends on the local circumstances at the notch influenced areas.

They may schematically be characterised by the local stress, strains or absorbed energy distribution as is shown in Fig. 2.

Fig 2. The stress distribution at the notch influenced area (scheme)

Fig 2. shows that the local circumstances at the notch vicinity can be characterised by three parameters, i.e. by the local maximum stress (loc), the length of the plateau of the maximum stress (l) and the gradient of stress (). Both of the two last parameters may be summarised with a single one denoted by XI (where the index I denotes the loading mode, i.e. the loading is perpendicular to the fracture surface). Using these parameters the notch stress intensity factor can be defined in the form of

KI =locXI (1)

The notch strain intensity factor (KI) and the notch energy intensity factor (KIw) can also be defined by the similar approach i.e.

KI= loc XI(2)

KIw = wloc XIw(3)

where loc and wloc are the local strain or energy concentrations, the XI and XIw the characteristic distances respectively. The local stress (loc), strain (loc) or energy (wloc) is proportional to the effective stress, strain or energy concentration factor.

In the case of a crack (i.e. notch radii is zero) in elastic media the value of KIis equal to infinity, because the local stress is also infinity (the stress field has a singularity). If the notch radii increases then the notch stress intensity factor decreases because the local stress concentration factor (Kt) at the notch vicinity in elastic media is proportional to the 1/, where is the notch radii, it can be predicted that a linear relationship exists between KI and as is illustrated by the straight line starts at the origin in Fig 3. If we look at the fracture surface it could be either brittle, or transition or totally ductile. It is obvious that the fracture parameters are different. They are either the plane fracture toughness (KIc) or the fracture toughness (Kc) respectively.

Fig. 3. Relationship between the notch stress intensity factor and fracture parameters

This is perfectly in agreement with the experimental observations, i.e. there exists a small notch radius by which brittle fracture of materials can be reached. This notch radius is denoted by 1crit . In this case the fracture parameter is the plane fracture toughness which is constant. If only the notch radius increases, the fracture has brittle-ductile transition character and upon reaching an upper limit of notch radius for instance 2critthe fracture is totally ductile. At these ranges the values of fracture parameter depend on ductile ratio in fracture surface i.e. the brittle tendency of materials can be characterised by the slope of the straight line as is shown in Fig. 4.

Fig. 4. The characteristic of brittle- ductile transition sensitivity of materials by the slope (tan  i) of 1/ KI vs. 

If the value of slope (tan  1) is small then the material is brittle, because the total brittle fracture can occur on a specimen with larger notch radius. In contrast, if the slope is high (tan 2) then the material is generally ductile, because the brittle fracture can only be found for a very small notch radius i.e. on a specimen with high notch acuity. The brittle-ductile transition

sensitivity of materials i.e. the slope (tan  i) of 1/ KI vs.  curve depends on

type of materials,
testing temperature and
loading rate.

In this paper only the grain size effect will be discussed as one of the material parameters.

2. Effect of grain size on brittle-ductile of mild steel

It is well known that by increasing the grain size the brittle-ductile transition sensitivity increases too. From the above mentioned approach it follows, that the slope (tan i) of 1/ KI vs.  curve increases with decreasing of grain size. This statement is reflected by Fig. 5.a. and Figure 5.b. constructed on the basis of experimental data [4].

Fig. 5. Effect of the ferrite grain size on fracture stress measured on notched low carbon steel specimens at -196 °C temperature.

a) Range b) for a given grain size

In accordance with Figure 4. the values of slopes (tan  i m) of 1/KI vs.  curves for different grain diameter (d) are plotted and is shown in Fig. 6.

Fig. 6. The value of slope (tan  i m) of 1/ KI vs. curves for different grain diameter (d)

Fig. 6. exactly shows that the grain size has a great influence on brittle-ductile sensitivity only in a given range of grain sizes i.e. ASTM GS N 2.0-4.1. If the grain size is high enough then its influence is not remarkable i.e. in the range of ASTM GS 2.0-4.1

In accordance with Fig. 3. the values of notch radii belongs to the beginning of brittle to ductile transition (1crit) for different grain size (d) are plotted and is shown in Figure 7.

Fig. 7. Critical notch radii (1crit) defined in Figure 3. vs. grain diameter (d) for mild steel tested at -196 °C.

Figures 6. and 7. are in full agreement with presented concept and they can be regarded as an experimental verification of the proposed approach for description of brittle-ductile behaviour of notched structural components.

Summary

1. The elastic-plastic deformation state of the notch influenced area can be characterised by local parameters by notch stress, strain or energy intensity factors.

2. The local parameters, the notch stress, strain and energy intensity factors are expressed by:

KI=globKX=locX

KI=globKX=locX

KIw=WglobKwXw=Wloc Xw

where the global stress, stain or deformation energy fields are characterised by,globgloband Wglob; the local fields at the notch tip are expressed by the local, K, K and Kw concentration factors and the distribution of these fields by characteristic distances, X , Xor Xw respectively.

3. The relationships between the notch intensity factors (KIi) and the notch radius (r) in 1/KIivs. co-ordinate system are linear for stress and strain (i= or ) and non-linear for deformation energy. The brittle-ductile transition sensitivity of materials can be characterised by the slope of 1/KIi vs.  curve.

4 The experimental results performed on notched tensile specimens made of mild steel with different grain size at -196 °C are in fully agreement with presented concept and they can be regarded as an experimental verification of the proposed approach.

Acknowledgment

The authors gratefully acknowledge the support for this work provided by the European Community (COPERNICUS programme 1994, Contract No. CIPA-CT94-0194, Co-ordinator: Professor G. Pluvinage) and the Hungarian National Foundation for Science (OTKA, Contract No T-15601).

References

[1] L.Tóth., H.Gouair., Z. Azari. and G. Pluvinage.: Notch effect on Brittle-Ductile transition. General Approach. (in Hungarian). GÉP.1994. 1994/4. 3-8.

[2] L.Tóth., G. Pluvinage, H. Gouair, Z. Azari.: The Notch Stress, Strain and Energy Concept. FRACTURE`94. University of Witwatersrand, Johannesburg. 23-24 November. Proceedings. Editor: M.N. James. 1994. 180-189.

[3] L.Tóth : Approach of the Brittle-Ductile Transition by the Concept of Critical Notch Stress, Strain or Energy Intensity Factor. Proc. of the 1st Workshop on " Influence of Local Stress and Strain Concentrators on the Reliability and Safety of Structures” Miskolc. 1995. 61-69.

[4] Y.Yokobori. and S. Konosu: Effects of Ferrite Grain Size, Notch Acuity and Notch Length on Brittle Fracture Stress of Notched Specimens of Low Carbon Steel. Engineering Fracture Mechanics, Vol. 9. 1977. 839-847.