A notched cross weld tensile testing method for determining true stress strain curves for weldments

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1 Engineering Fracture Mechanics 69 (2002) A notched cross weld tensile testing method for determining true stress strain curves for weldments Z.L. Zhang a, *, M. Hauge b, C. Thaulow a, J. Ødegard a a SINTEF Materials Technology, Rich. Birkelands vei 1C, N-7465 Trondheim, Norway b Statoil Research Centre, N-7005 Trondheim, Norway Received 31 January 2000; received in revised form 18 June 2001; accepted 21 June 2001 Abstract Cross weld tensile testing is widely used in the industry to qualify welds. In these conventional testing fracture load is measured and the location of fracture (weld metal, base metal or heat affected zone) is evaluated. Because the loadelongation curve depends on the location of fracture and the initial gauge length, it cannot be utilized in the failure assessment of weldments. Failure assessment of weldments requires input of true stress strain behaviour for each material zone. In this paper, a notched cross weld tensile testing method is proposed for determining the true stress strain curve for each material zone of a weldment. In the proposed method, cylindrical cross weld tensile specimens, with a notch located either in the weld metal, base metal or possibly heat affected zone are applied. Due to the notch, plastic deformation is forced to develop in the notched region. A load versus diameter reduction curve is recorded. It has been shown that the true strain at maximum load is independent of the notch geometry. Furthermore, the materials true stress strain curve can be determined from the recorded load versus diameter reduction curve of a notched cross weld tensile specimen by dividing a geometry-factor G, which is approximated by a quadratic function of the specimen diameter to notch radius ratio and a linear function of the true strain at the maximum load. It is found that G is independent of the material zone length when the homogenous material length is larger or equal to the minimum diameter. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Load-separation principal; True stress strain curve; Weldment testing and mismatch effect 1. Introduction For homogenous thin materials, a method has been recently developed to determine the long range true stress strain curve by using tensile specimens with rectangular cross section [1]. This paper presents a new method for weldments. Weldments are inhomogenous in nature. The mechanical properties of base metal, weld metal and heat affected zone (HAZ) are different to each other. Assessment of failure behaviour of weldments requires input of full-range true stress strain curve for each material zone. Testing of weld thermal simulated specimens and all weld tensile testing can be carried out. However, cross weld tensile * Corresponding author. Tel.: ; fax: address: zhiliang.zhang@matek.sintef.no (Z.L. Zhang) /02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S (01)

2 354 Z.L. Zhang et al. / Engineering Fracture Mechanics 69 (2002) Nomenclature r flow stress r n nominal stress, P=A 0 r z true tensile stress, P=A e true tensile strain P tensile load P max maximum tensile load A current cross section area A 0 initial cross section area D 0 initial diameter of the minimum notched cross section H material zone length R 0 initial notch radius G geometry factor r 0 yield stress r Pmax true stress at the maximum load e Pmax true strain at the maximum load Bridgman corrected true stress r B testing of weldments is cheap and attractive. Cross weld tensile testing has been widely used in the industries to qualify welds, i.e. whether the failure occurs in the base metal that represents a good scenario, or in the weld metal or HAZ that is often not wanted. In cross weld tensile testing, load versus elongation in the axial direction can be recorded (Fig. 1). For obvious reasons, the load versus elongation curve cannot be utilized in the assessment of failure behaviour of weldments. The curve is strongly dependent on the initial measuring gauge length, the sampling of materials, and the location of necking and final fracture. In practice the actual strain in different material zones can be measured during cross weld tensile testing, by attaching strain gauges to the materials or using optical measurements. The application of these methods was very limited because of the nature of these measurements. The surface strains and deformation cannot be directly transferred to materials full range stress strain curve. The limitations of the current weldment testing methods necessitate the development of alternative testing method. In this paper, a new method called notched cross weld tensile testing has been proposed to determine materials true stress strain curve for each material zone. In this method tensile specimens with a Fig. 1. (a) Conventional cross weld tensile testing, and (b) typical outputs for initial different gauge length.

3 Z.L. Zhang et al. / Engineering Fracture Mechanics 69 (2002) Fig. 2. Proposed notched cross weld tensile specimen. round notch located in the middle of a material zone are tested in tension. Fig. 2 schematically shows the notched cross weld tensile testing specimens proposed in the paper. Load versus diameter reduction is recorded for each test. It has been shown by an extensive numerical study that smooth and notched tensile specimens reach the maximum load at the same true strain. And materials true stress strain curve can be obtained based on the so-called load separation principle, by normalizing the load diameter reduction curve by a geometry factor. The effect of notch geometry, material length as well as hardening behaviour on the accuracy of the method has been investigated. 2. The load separation principle In fracture mechanics, there is a so-called load separation principle [2] which states that the load deformation behaviour of a fracture mechanics specimen can be represented by a multiplication of two parts. The first part, g, is a function of geometry, while the second one, h, is a function of plastic displacement which represents the hardening behaviour of a material, P ¼ gða=wþhðv p =wþ; ð1þ where P is the load, a is the crack length, w is the specimen width and v p is the plastic displacement, for example, the load line plastic displacement. The load separation principle is the theoretical basis for ASTM standard test method for J 1c and J R curve from single specimens [3,4]. It should be noted that Eq. (1) most often is used before the maximum load or possibly after the maximum load for the cases where the maximum load is caused by crack growth rather than by diffused necking. The load separation principle is very interesting in that the material function h once obtained from a specific geometry can be transferred to any other geometry, because the material is the same. Recent studies [5] have shown that with modifications the load separation principle works satisfactory for many examples, and the plastic displacement function can be transferred from one geometry to another. Moreover, it has been suggested that plastic displacement function can be linked to notched cylindrical tensile specimens [6,7].

4 356 Z.L. Zhang et al. / Engineering Fracture Mechanics 69 (2002) The idea of this paper is based on the load separation principle. The authors are generally interested in obtaining both the tensile properties and fracture toughness for weldments by using alternative and simple testing methods. This paper is a first step towards an alternative testing method. It will explore the possibility of determining the true stress strain curve for different material zones of a weldment by using a round notched cross weld tensile specimen. When applying the load separation principle, several critical questions should be asked, namely, how the notch geometry influences the geometry function g, whether the geometry function is dependent on materials hardening behaviour, and what is the effect of material zone length. These questions have been answered in the following sections. 3. Numerical procedure A series of notched specimens have been analysed by ABAQUS for materials with various hardening ability and zone length. Fig. 3 shows the representative finite element meshes used for the specimens. The minimum diameter for the tensile specimens is 6 mm. Eight-node axi-symmetric elements were used. The total number of elements varied from 530 to Fig. 3. Meshes for the (a) smooth specimen, (b) notched specimens.

5 Z.L. Zhang et al. / Engineering Fracture Mechanics 69 (2002) The elastic properties for the materials considered in the paper are taken as E=r 0 ¼ 500 and m ¼ 0:3. A power-hardening law material with finite strain theory was applied to the analyses. For the material, r ¼ r 0 1 þ ep e 0! n ; ð2þ where r is the flow stress, e p is the equivalent plastic strain, r 0 is the yield stress, e 0 is the yield strain e 0 ¼ r 0 =E, and n is the strain hardening exponent. Materials hardening considered in the paper varies from n ¼ 0: Instability of notched tensile specimens The strain at maximum load is an instability parameter of the tensile specimen. In this section we will show theoretically that this parameter is independent of the constraint. Thus, the strain at maximum load should be the same for different notch configurations. The numerical results are used to verify this hypothesis. Consider two unit cells, one with uniaxial loading and one with triaxial loading, Fig. 4. The first one (Fig. 4(a)) represents the smooth tensile specimen where the transversal stress is zero, and the latter (Fig. 4(b)) represents the notched tensile specimen where the transversal stress is proportional to the axial stress. The instability for Fig. 4(a) occurs when the following condition is satisfied [8] dp ¼ dðr z AÞ ¼ Adr z þ r z da ¼ 0; ð3þ where P is the tensile load and A is the current cross section area of the unit cell. From Eq. (3) we obtain dr z ¼ da r z A : ð4þ In the case of uniaxial tension, the left side of Eq. (4) becomes dr=r, where r is the flow stress. The right side can be approximated by the equivalent strain increment de, such that the instability condition becomes: Fig. 4. Unit cells illustrating the conditions at the maximum load. c is a constant less than 1.0.

6 358 Z.L. Zhang et al. / Engineering Fracture Mechanics 69 (2002) dr de ¼ r: ð5þ For notched tensile specimens (Fig. 4(b)), Eq. (4) is still valid. By neglecting the elastic component of the strain, the right side of Eq. (4) is also in this case equal to the equivalent strain increment de. However, r z is not equal to the flow stress, but r z ¼ r=ð1 cþ. Nevertheless, by substituting this relation to Eq. (4), we can again obtain Eq. (5). For smooth specimen and power law hardening material, diffuse necking will follow the maximum load and the strain at the maximum load is equal to the hardening exponent [8] e Pmax ¼ n: ð6þ Eq. (6) and the above explanations show that the strain at maximum load is an unique material parameter, independent of the geometrical constraint and equal to the strain hardening exponent if a power law hardening material is considered. In the numerical study, specimens with a material with n ¼ 0:1 have been studied first. This material has also been used as a reference material in the next stage where the effect of material hardening behaviour on the accuracy of the method is considered. Fig. 5(a) shows the normalized gross stress versus true strain curves for three notch configurations. The figure confirms that maximum load occurs at the same strain level for all the geometries and that this strain is equal to the strain hardening exponent. However, it appears also that the exact value of this strain can be difficult to determine, especially for the smooth specimen. It must be noted that Eq. (5) is only valid approximately, because the elastic strain has been neglected. So does Eq. (6). 5. True stress strain curve from smooth and notched tensile specimens homogenous material Fig. 5(b) shows the true stress strain curves for three cylindrical tensile specimens with different notch configurations. The true stress is calculated by dividing the current load by the area of the current minimum notch cross section. Difference between the gross stress and the true stress becomes significant only after the diffuse necking has occurred. It should be reminded that Fig. 5(a) represents the behaviour of the same material but different geometry. The conventional way of transferring material data is to determine the flow stress strain relation from the true stress strain curve of smooth specimens by the Bridgman correction [9]. Then, the flow stress can be transferred to the prediction of the notched specimens. Here in this paper, we invert this concept. Fig. 5(b) shows that the slope of the true stress strain curves for notched specimens are very similar to those for the smooth specimens. A normalization procedure has been applied to the true stress strain curves shown in Fig. 5(b), i.e. all the curves are normalized by their true stress at maximum load. The results of the normalization are presented in Fig. 5(c). It is interesting to observe from Fig. 5(c) that, to a large degree, the three curves are collapsed into one over a quite large range of strain. It should be noted that the strain at the maximum load for the material used in Fig. 5 is 0.1. The normalized curves are also plotted in Fig. 5(d), where the true strain has been normalized by the true strain at the maximum load. In line with the load separation principle discussed in Section 2, the true stress strain curve for a notched tensile specimen (Fig. 5) can be expressed by a multiplication of the true stress strain curve of a smooth specimen and a geometry factor G: r Notched z ðeþ ¼Gr Smooth z ðeþ: ð7þ From the above equation, materials true stress strain curve represented by the smooth specimen can be obtained from the true stress strain curve of a notched specimen by r Smooth z ðeþ ¼r Notched z ðeþ=g: ð8þ

7 Z.L. Zhang et al. / Engineering Fracture Mechanics 69 (2002) Fig. 5. Results for tensile specimens with n ¼ 0:1: (a) normalized gross stress versus true strain, (b) normalized true stress versus true strain, (c) true stress normalized by the stress at maximum load versus true strain, (d) normalized true stress versus strain normalized by the strain at maximum load. Eq. (8) is schematically shown in Fig. 6(a) and (b). It must be noted that the geometry correction is simply applied to the stress, rather than the strain. The general observation of the normalized curves is that the difference between the smooth specimen and the notched specimens before the maximum load is very small. After the maximum load, however, the true strain is slightly amplified for the notched tensile specimens, compared with the smooth specimen. This effect comes from the strain concentration at the notch position. Fig. 5 shows that the true stress strain curve estimated from the notched specimens is conservative. By carrying out a number of analyses of notched specimens for material with hardening n ¼ 0:1, we obtain the following approximate relation for the geometry factor G (n ¼ 0:1), G ¼ 1:007 þ 0:18777 D 0 R 0 0:01313 D 0 R 0 2 ; ð9þ where D 0 and R 0 are the initial diameter and notch radius. Eq. (9) is plotted in Fig. 6(c).

8 360 Z.L. Zhang et al. / Engineering Fracture Mechanics 69 (2002) Fig. 6. A schematic plot of the proposed method. The true stress curve from a notched specimen (a), to the true stress strain curve of the material (smooth specimen) (b,c) the geometry factor G versus the initial diameter/notch radius ratio. It should be reminded that the true stress strain curve is not the flow stress strain relation used in finite element analyses. A Bridgman correction should be applied to the true stress strain curve obtained from a notched tensile specimen [9]: r B ¼ r Smooth z =Bðe e Pmax Þ; ð10þ where B is the Bridgman correction factor which is a function of the net strain after necking, e e Pmax. Material s flow stress-equivalent plastic strain curve can be obtained from the r B e curve by separating the plastic strain from the true strain. 6. Effect of material hardening exponent Eqs. (8) and (9) are based on the material with hardening exponent n ¼ 0:1. It is important to know how the geometry function G in Eq. (8), is influenced by the material hardening behaviour. Materials with different hardening exponents have been studied with the smooth and notched specimens. Fig. 7(a) shows the normalization for a material with n ¼ 0:2. It can be seen that the normalization works very well for this

9 Z.L. Zhang et al. / Engineering Fracture Mechanics 69 (2002) Fig. 7. True stress strain curves for n ¼ 0:2. The true stress strain curve for the three specimens (a), and the normalized curves (b). material before the maximum load, and even better than the material with n ¼ 0:1. Similar results can be seen in Fig. 8 for a low hardening material with n ¼ 0:05. The general conclusion is that the normalization is better for high hardening materials than for low hardening materials. The effect of hardening on the geometry factor has been studied. The difference, ðg n G n¼0:1 Þ=G n¼0:1 versus hardening exponent is shown in Fig. 9(a), where the material with n ¼ 0:1 has been taken as the reference material. It seems that the hardening will affect the geometry function. The error for the strong hardening material with n ¼ 0:2 can be up to about 8% when the geometry factor from the reference material with n ¼ 0:1 is used. It is obvious that the error of the geometry is dependent on the sharpness of the notch. For the geometry with D 0 =R 0 ¼ 3:0, the error is much smaller, less than 4%. It should be mentioned that the reason to apply a notch in the tensile specimens is to force the plastic deformation localized in the material zone of interest. It is not necessary to use sharp notch geometry. Results from this Fig. 8. True stress strain curves for n ¼ 0:05. The true stress strain curve for the three specimens (a), and the normalized curves (b).

10 362 Z.L. Zhang et al. / Engineering Fracture Mechanics 69 (2002) Fig. 9. (a) Relative difference, ðg n G n¼0:1 Þ=G n¼0:1 as a function of hardening exponent e Pmax, (b) G n =G n¼0:1 versus e Pmax. study shows that when the notch radius to diameter ratio D 0 =R 0 is larger than 3.0, quite good accuracy in engineering sense will be achieved. Fig. 9(b) plots the G n =G n¼0:1 ratio versus different hardening for the notch geometry D 0 =R 0 ¼ 3. A linear equation can well fit the G n =G n¼0:1 hardening relation: G n ¼ 1:053 0:53e Pmax : ð11þ G n¼0:1 By combining Eqs. (9) and (11) we obtain the following approximate equation for calculating the geometry factor G, " G ¼ 1:007 þ 0:18777 D 0 0:01313 D # 2 0 ð1:053 0:53e Pmax Þ: ð12þ R 0 R 0 7. True stress strain curve from notched cross weld tension effect of material zone length So far the focus has been the specimens with homogenous material. This section will focus on weldments. The conventional cross weld tensile testing uses specimens with rectangular cross section. In the notched cross weld tensile testing, specimens with round cross section will be used. A bi-material specimen (weld metal and base metal) is considered. For smooth bi-material specimen, necking will occur either in the weld metal or in the base metal, depending on the mismatch of yield stress, hardening ability and boundary conditions. When a notch is applied to the centre of a material zone (Fig. 2) plastic deformation will be localized in the notched zone, no matter undermatch or overmatch the notched zone material is. The effect of the material zone length on the true stress strain curve of a notched specimen is investigated for a bi-material case where the material in the notched region has lower stress strain curve than the surrounding material. In particular, the required length of the notched zone to behave as a homogenous specimen is evaluated. Five notched specimens with different material zone length have been analysed. Fig. 10(a) shows the gross stress versus true strain curves for different material zone length for the case with D 0 =R 0 ¼ 3:0,

11 Z.L. Zhang et al. / Engineering Fracture Mechanics 69 (2002) Fig. 10. Effect of material zone length on the stress strain curve of a bi-material specimen with D 0 =R 0 ¼ 3:0. Gross stress versus strain (a), and true stress versus strain (b). The material system is characterized as n ¼ 0:1 and m ¼ 0:5. hardening exponent n ¼ 0:1, and material mismatch ratio m ¼ 0:5. The m is defined as the ratio of weld metal yield strength (notch material) to the base metal yield strength. The general observation is that short material zone will increase the gross stress for a given true strain. The effect of material zone length is similar to the effect of notch radius, short material zone length corresponds to small notch radius. Material zone length enforces a material plasticity constraint to the specimen, while the notch representing a geometry constraint. Both the geometry and material constraint enhance the hydrostatic stress in the notch region. As discussed in Section 4 above, the hydrostatic stress component does not influence the true strain at the maximum load. Fig. 10(a) shows that the true strain at the maximum load is independent of the material zone length H. The effect of the material zone length on the true stress strain curve is shown in Fig. 10(b). It can be observed that when the zone length is close to or larger than the diameter at the notch cross section, the bimaterial specimens behave like a homogenous specimen, and the effect of zone length on the resulting true stress strain curve becomes insignificant. Similar observation has been observed for cases with different ratios of specimen diameter/notch radius, see Fig. 11 for D 0 =R 0 ¼ 7:5. This finding is in accordance with the observation of Toyoda [10]. Toyoda found that for a bi-material specimen, the homogenous behaviour becomes dominant when the zone length is larger than the minimum diameter. The effect of material mismatch on the true stress strain curve has also been investigated. When the ratio of the initial notch radius to the initial minimum diameter is larger than 1.0, the absolute value of mismatch has almost no effect on the true stress strain curve. Example is shown in Fig Discussion and concluding remarks It has been found in this study that true stress strain curves for a given material from both smooth and notched tensile specimens can be normalized by a respective geometry factor, such that the normalized curves collapse into one. The geometry factor has been approximated as a quadratic function of notch geometry parameter D 0 =R 0, and a linear function of the true strain at the maximum load. It should be noted that this normalization covers a wide range of strain after the maximum load has appeared. This finding gives a basis for an alternative testing method for determining material true stress strain curve by using the

12 364 Z.L. Zhang et al. / Engineering Fracture Mechanics 69 (2002) Fig. 11. Effect of material zone length on the true stress strain curve of a bi-material specimen with D 0 =R 0 ¼ 7:5. The material system is characterized as n ¼ 0:1 and m ¼ 0:5. Fig. 12. Effect of mismatch on the true stress strain curve for D 0 =R 0 ¼ 3:0, and H=D 0 ¼ 1:67 and n ¼ 0:1. notched tensile specimen. Notched tensile specimens have the advantage to force the plastic deformation localised in the region of interest, such that one can always test the material intends to test. One interesting finding from this study is that the strain at maximum load is rather independent of the notch geometry and material zone length. Instability analysis shows that the strain at maximum load is a very good indicator of material hardening behaviour. In many cases, not the whole stress strain curve but the hardening is of interest. Thus the simple notched cross weld tensile testing can give very accurate hardening parameter. In this study only bi-material systems have been considered. The method can be in principle applied to multi-material system, for example to the testing of HAZ material in weldments, as long as the HAZ mechanical properties are uniform over a certain length. The diameter can be adjusted to satisfy the condition that the material zone length is equal to or large than the diameter. In the interpretation of HAZ testing results, care should be taken how representative the sampled HAZ is. HAZ usually has a strong gradient from the fusion line to the base metal. The typical length of steel HAZ is about 2 mm, while the

13 Z.L. Zhang et al. / Engineering Fracture Mechanics 69 (2002) Fig. 13. True stress strain curves for n ¼ 0:1 material at the beginning of loading. aluminium HAZ length can be as large as 10 mm. Direct testing of tensile specimens with notch positioned in the HAZ may give representative properties. Finally, it should be mentioned that results in this study show that the load separation is successful in a global sense for tensile specimens. Fig. 13 shows the true stress strain curve for smooth and notched tensile specimens with material n ¼ 0:1 within the strain range 1%. It can be seen that the yielding pattern for the smooth one and the notched ones are very different. Smooth specimen has a very sharp transition from elastic behaviour to plastic yielding because the material has a uniform stress state. Once one material point starts yielding, the whole specimen is yielding. However, the transition to plastic yielding is rather smooth for the notched specimens. Only part of the material will yield in the beginning and other part is still elastic. This makes the transition smooth. Strictly speaking, the three curves within 1% of strain cannot be normalized. If the strain gradients are different in different tensile specimens, the load separation principle is in a strict sense not applicable. Therefore, the load separation principle is generally valid only in an approximate sense. Acknowledgements The financial support from the Norwegian Research Council through the Strategic Institute Programme at SINTEF Materials Technology is greatly appreciated. References [1] Zhang ZL, Hauge M, Ødegard J, Thaulow C. Determining material true stress strain curve from tensile specimens with rectangular cross section. Int J Solids Struct 1999;36: [2] Ernst HA, Paris PC, Rossow M, Hutchinson JW. In: Smith CW, editor. Analysis of load-displacement relations to determine J R curves and tearing instability material properties. Fracture Mechanics ASTM STP p [3] ASTM E813 Standard test method for J 1c, a measure of fracture toughness, ASTM annual book of standards v 03.01, [4] ASTM E1152 Standard test method for determining J R curve, ASTM annual book of standards v 03.01, [5] Cruz JR, Landes JD. A common format approach for the ductile fracture method using a displacement-based normalization parameter. Fatigue Fract Engng Mater Struct 1997;20:

14 366 Z.L. Zhang et al. / Engineering Fracture Mechanics 69 (2002) [6] Donoso JR, Labbe F. A calibration function for notched cylindrical tension specimens, based on the common format equation: numerical and experimental data analysis. Engng Fract Mech 1996;54: [7] Donoso JR, Landes JD. The common format equation approach for developing calibration functions for two-dimensional fracture specimens from tensile data. Engng Fract Mech 1996;54: [8] McClintok FA, Argon AS. Mechanical behaviour of materials. USA: Addison-Wesley Publishing Company; [9] Bridgman PW. Studies in large plastic flow and fracture. New York: McGraw-Hill; [10] Toyoda M. Plastic constraint controlling factors and their effect. 2nd Workshop on Constraint Effects on Structural Performance of Welded Joints, Osaka, Japan, 1994.