4th International Congress
of Croatian Society of Mechanics
September, 18-20, 2003
Bizovac, Croatia /
FRACTURE BEHAVIOUR OF HIGH-DUCTILE CCT SPECIMEN
UNDER ELASTIC-PLASTIC CONDITIONS
Franjo Matejiček, Dražan Kozak, Pejo Konjatić
Keywords: / CCT Specimen, J-integral, crack growth, J-R curve, crack driving force, FE analysis
1. Introduction

When cracks are identified in structures or components during service, they must be evaluated to determine suitability for continued operation. Fracture mechanics provides a methodology evaluating the structural integrity of components containing such defects, and demonstrating whether they are capable of continued, safe operation.

In assessing the integrity of structures containing cracks, it is important to quantify the relevant crack-driving force, so that its load carrying capacity can be predicted. For ductile materials permitting large-scale plasticity near the crack tip, this crack-driving force is frequently described as contour J-integral [1], which is one appropriate elastic-plastic fracture mechanics (EPFM) parameter (in absence of constraint effects) of low-strength and high-toughness materials.

However, it is not enough to determinate the value of J-integral to be able to describe the fracture behaviour fully, especially for materials with high ductility [2]. It is necessary also to measure the crack growth during the test. This enables the drawing of the crack growth resistance curve (R curve), which may be considered as the material property just under J-controlled fracture.

If there is excessive plasticity or significant crack growth, fracture toughness may depend on the size and geometry of the test specimen [3]. Therefore, J-integral as a single parameter characterizes crack tip conditions only under small scale yielding (SSY). McClintock [4] applied slip line theory to estimate the stresses in a variety of configurations under plane strain, fully plastic conditions. The results indicate that, for a non-hardening material under fully yielded conditions, the stresses near the crack tip are not unique, but depend on geometry. Thus a deeply notched double-edged notched tension (DENT) panel or a single-edged cracked panel in bending (SENB) maintain a high level of triaxility, such that the crack tip conditions are similar to the SSY case. On the other hand, a center cracked panel in pure tension (CCT) is incapable of maintaining significant triaxility under fully plastic conditions.

Therefore, methodology for J-integral and crack length estimation of a CCT specimen made of high ductile stainless steel is presented in this paper. Estimation is conducted using results gained by experiments and it was confirmed using finite element analysis (FEA).

2. J-controlled crack growth

The value of J-integral may be determined directly on the fracture toughness specimen, attaching an array of strain gages in a contour around the crack tip [5], but the instrumentation required for such experimental measurements is highly cumbersome.

In general, the J-integral for a variety of configurations can be written in the following form:

/ (1)

where Uc defines the work done under the applied stresses in the vicinity of the crack in an elastic-plastic stress and strain field, η is dimensionless constant (η = 2 for a deeply cracked plate), B is the thickness of the specimen and b is the ligament size (b = W - a). Equation (1) can be separated into elastic and plastic components:

/ (2)

where KI presents the linear elastic stress intensity factor, E*=E for plane stress and E*=E/(1-ν2) for plane strain conditions. In its simplest form, the material resistance in EPFM regime is measured by the elastic-plastic fracture toughness (JIc). Because of the ductile nature of materials in the EPFM regime, there may also be considerable stable crack extension of the material even when the applied JI reaches the JIc value. Hence, another material resistance property becomes important in this regime. This property is represented by the J-Resistance (J-R) material curve, which measures the resistance of the material to stable tearing. Comparison of applied JI versus the J-R curve allows the determination of the crack size or stress at which unstable tearing occurs. Anyway, one should be careful by interpretation of obtained results, because J controlled conditions exist at the tip of a stationary crack only if the large strain region is small compared to in-plane dimensions of the cracked body (Fig. 1).

Figure 1. J-controlled crack growth

Otherwise, we might expect J integral theory to break down when there is a combination of significant plasticity and crack growth. Namely, when the crack grows out of the zone of J dominance, the measured R curve is no longer uniquely characterized by J. Whereas crack initiation is fairly independent of test variables which affect the constraint, the R curve of a given material depends largely on the stress state ahead of the crack tip. Thin-walled structures represent a simpler situation: plane stress conditions prevail, generally characterized by the development of full shear fracture, the R curve is fairly independent of variables like specimen size and a/W ratio.

According to [3] a valid J-R curve in the plane stress case can only be obtained up to about:

/ (3)

where Δa* and b0 denote the crack growth at R-curve splitting (crack extension after initiation point) and starting ligament length, respectively.

The parameter, which has less stringent limitations than the J-integral, is the CTOD in terms of d5 [6]. It is measured at the tip of the fatigue pre-crack with a gauge length of 5 mm. This method has the great advantage that d5 can be directly measured on any specimen configuration and because of that it was used in this work.

3. CCT specimen testing

Research was conducted on specimens made of stainless steel X 5 CrNi 18 10, with yielding strength of Rp0,2=250 MPa and stress of 620 MPa by elongation of about 16%. While testing was conducted important parameters were measured graphically using chart writer and digitally using computer. First series of tests were conducted on specimens prepared for classic tension test (Figure 2a) to determine real characteristics of material including σ-ε diagram, and after on standard CCT specimens shown on Figure 2b, with 2a/W = 10/30 = 0,3.

a) tension test specimen / b) CCT specimen
Figure 2. Tension test and CCT specimen

True stress – strain curve determination is very important for numerical simulation, because well described material yielding law directly influences the accuracy of FE results. According to standard procedure, CCT specimens were fatigued to realise the pre-crack with desired extension (Fig. 3). Its amount was about 2,5 mm at each notch end. During testing, behind the force F, three characteristic displacements were measured: load line displacement (LLD), crack mouth opening displacement (CMOD) and crack tip opening displacement CTOD (δ5).

Figure 3. Crack extension

Single specimen method with loading-unloading compliance technique is used to determine compliance of material and crack resistance curve J-Δa. Specimens were partially unloaded (to 60% of applied force) and then reloaded in intervals during the test. Test was conducted on three CCT specimens. Two of them were needed to demonstrate accuracy of the equipment at small and intermediate amounts of crack growth [7]. Total crack growth during the test was estimated as the difference between initial and final crack length. The final crack length after testing was found as average value of nine length measurements (Fig. 4) through the thickness [8]:

/ (4)
Figure 4. Crack length measurement

Compliance of material also had to be determined from changing of the loading-unloading slope in F-CMOD curve intervals. Knowing compliance in the first cycle and in final cycle of test and assuming that alteration of compliance and crack extension is linear (Figure 5) makes possible to determine crack length at any stage of test.

Figure 5. Compliance vs. crack extension

Considering this assumption, crack extension is determined for characteristic points in F-LLD diagram. Since material used for this experiment possesses high ductility, effect on compliance of material at the beginning of test had to be analysed. That means that compliance first decreases then reaches a minimum and finally increases. Some authors [9] consider that minimum along the C=f(LLD) curve (if detected) may be identified as the onset of crack growth.

J-integral for CCT specimen has been calculated measuring area under curve in F-LLD diagram representing plastic and elastic component of work and using expression [10]:

/ (5)

Using calculated J-integral and crack growth obtained through measured compliance for characteristic stages of test, crack growth resistance curve J-Δa was made according to ASTM E 1152 [11]. It is a typical J resistance curve for a ductile material. In the initial stages of deformation, the R curve is nearly vertical; there is a small amount of apparent crack growth due to blunting. As J increases, the material at the crack tip fails locally and the crack advances further. One measure of fracture toughness, JIC is defined near the initiation of stable crack growth Ji. The determination of Ji requires the use of a scanning electron microscope (SEM) to measure the stretch zone width (SZW) on the fracture surface of the specimen, but this method can produce large scatter. Therefore, it is often in engineering practice that only J0,2BL could be determined corresponding to the fracture resistance at 0,2 mm of ductile crack growth [12]. This procedure will be shown later (Fig. 9).

4. Finite element modelling

A three-dimensional final element model of CCT specimen was prepared for finite element analysis in Ansys code [13]. One eights of specimen is used for modelling to take advantage of symmetry (Figure 6).

Figure 6. Finite element model of 1/8 of CCT specimen

The finite element mesh was scaled closer to the tip of crack and to the place where crack will propagate than to other areas of specimen (Figure 7). Finite element model with 16780 elements and 79392 nodes was used. Quasi-static load is applied to model to simulate loading-unloading technique used in experiments. At every point of unloading, crack growth is added to initial crack length to simulate actual crack propagation. That was accomplished by “node releasing” technique. First nine time steps were performed simulating five loadings and four unloadings giving enough data to compare obtained results with experiment.

Figure 7. Finite element mesh
5. Results of finite element analysis

Comparison of the results for 3-D element model and experimentally evaluated results is shown in Figures 8 and 9. As it can be seen simulation results are matching to results obtained by experiment, which indicates that earlier mentioned assumptions can be considered valid in this case. For equivalent load line displacement, force used in experiment and force obtained by simulation differs in no more than 10% (Figure 8). First nine cycles were simulated containing first four crack propagation and it can be seen from J-Δa diagram (Figure 9) that experiments and simulation also shows good match. Specimen after last stage of experiment (breaking), shown on Figure 10 is compared to last stage of numerical analysis. Red line showing crack mouth, which can be seen on finite element model on the right side, indicates similarity of deformed shape of the specimen.

Figure 8. Experimental and numerical F-LLD curves
Figure 9. J vs. Δa curve
Figure 10. Crack mouth photo and FE simulation of dimple making
6. Conclusions

Centre cracked tensile (CCT) specimens made from high-ductile steel are not often the matter of concern in fracture behaviour investigations. It can be expected that such materials show very good crack resistance with large stable crack extension. Also, it is well known that geometry of CCT specimen is less sensitive to constraint effects and tension is more desirable type of loading than bending. Due to fact that existence of SSY in this case cannot be expected, obtained J-integral values should be considered very careful.

However, if the crack growth is J-controlled, what means that J-zone is predominant, the J-R curve may be taken as valid. Conditions, which should be satisfied according to [3] are that analysed structure has to be thin (plane stress state prevails) and achieved crack extension has not to be over 20-30% of the ligament size. This condition is fulfilled in our investigation and therefore, J-R curve might be considered as material property.

Finite element simulation show very good agreement between experimental and numerical results and it can be applied to draw crack driving force, what is of great importance when the critical length of crack or critical applied stress should be determined.

Acknowledgement

Authors would like to thank to the Ministry of Science and Technology of Republic of Croatia for the support of their investigations through the project 0152018 'The life assessment of structure components by using of fracture mechanics principles'.

References
7. References

[1]  Rice, J.R.: “A path independent integral and the approximate analysis of strain concentrations by notches and cracks”, Journal of applied mechanics, Vol. 35, 1968, pp. 379-386.

[2]  Anderson, T.L., “Fracture Mechanics: Fundamentals and Applications”, CRC Press, 1995.

[3]  Schwalbe, K.H., “Ductile crack growth under plane stress conditions: size effects and structural assessment – I. Size and geometry effects on crack growth resistance”, Engineering Fracture Mechanics, Vol. 42, No. 2, 1992, pp 211-219.

[4]  McClintock, F.A., “Plasticity Aspects of Fracture”, Fracture: An Advanced Treatise, Vol. 3, Academic Press, New York, 1971, pp. 47-225.

[5]  Read, D. T, “Applied J-Integral in HY130 Tensile Panels and Implications for Fitness for Service Assessment”, Report NBSIR 82 – 1670, National Bureau of Standards, Boulder, Colorado, 1982.

[6]  Hellmann, D. and Schwalbe, K.-H., “Geometry and size effects on J-R and d-R curves under plane stress conditions”, ASTM STP 833, 1984, pp. 577-605.

[7]  Schwalbe,K.-H., Neale, B. K., Heerens, J., “The GKSS test procedure for determining the fracture behaviour of materials: EFAM GTP 94”, GKSS-Forschungszentrum Geesthacht GmbH 1994, pp 75.

[8]  ESIS P1-92, ESIS recommendations for determining the fracture resistance of ductile materials, 1992.

[9]  Neimitz, A., “A phenomenological model of the elastic-plastic CCT specimen containing a growing crack”, Enfineering Fracture Mechanics 68, 2001, pp 1219-1239.