MICRO-MECHANICAL DAMAGE MODELLING OF NOTCHED BAR TESTING OF MODERN LINE PIPE STEEL

Transcription

1 MICRO-MECHANICAL DAMAGE MODELLING OF NOTCHED BAR TESTING OF MODERN LINE PIPE STEEL S. H. Hashemi, I. C. Howard, J. R. Yates and R. M. Andrews * The University o Sheield, Department o Mechanical Engineering, Sheield, UK * Advantica Technologies Ltd, Loughborough, UK s.h.hashemi@she.ac.uk Summary This paper reports work on the modelling o lat racture in modern gas pipeline steels. Experimental data rom typical tensile bars together with damage mechanics theories has been used to capture lat racture characteristics o gas pipeline steel o grade API X100. This is required or subsequent analysis o Charpy impact specimen to isolate that part o the absorbed energy associated with lat racture appearance on the centre o the Charpy racture surace. The results o this study showed that typical damage parameters o the modiied Gurson model or ductile racture are applicable to high-grade X100 steel. The numerical analysis was able to simulate the necking o all tensile specimens. However, a small value o void volume raction was required to trigger the damage in the centre o FE model where the stress triaxiality was high. The inal stage o crack propagation in test samples was dominated by slant racture. An average stress triaxiality o 0.88 was able to characterise the onset o the lat-to-slant racture transition in all tensile specimens. The speciic lat racture energy was 1.0 J / mm or this steel. Introduction A major concern or the designers and operators o high-pressure gas transmission pipelines made rom high-strength steels is the control o long running ductile ractures. Current practice is to control racture propagation by speciying an upper shel Charpy energy using various semiempirical models. Full-scale racture propagation tests on modern high-strength steels, or example Demoonti et al. [1], have shown that these models become increasingly inaccurate as the steel strength increases. It has been revealed that propagation/arrest prediction models based on total Charpy absorbed racture energy require extremely high levels o material racture toughness or X100 steel (o the order o 400J or above in terms o Charpy impact energy) which is physically impractical []. This has led to dierent amendments and use o various correction actors or a better correlation between the test and the prediction model [3]. However, the Charpy test data actually does contain inormation connected with the pipeline ailure mechanisms. Typically the Charpy racture surace on the upper shel contains lat racture at the centre and shear lips at the edges. Hence a potential way orward is to isolate the part o the Charpy energy that is associated with the slant shear racture, discarding the lat racture inormation and other eects such as overall plastic deormation. To do this, accurate models o the lat and slant racture processes are required. The research reported here describes recent results on the modelling o the lat racture in high-strength pipeline steel o grade API X100. Details o the test and computational work on

2 slant racture o the X100 steel are set out in reerence [4]. In the current work, the experimental load-diametral contraction data rom tensile bars was used together with damage mechanics theories to model the racture characteristics o the test specimens. Although the material was anisotropic (due to the pipe rolling schedule), an isotropic axi-symmetric inite element model was able to simulate the mean load-diametral variation in the pipe thickness direction. Typical Gurson damage parameters or lat racture proved to be applicable to high-strength low-alloy X100 steel. However a small critical void volume raction o the order o was needed to trigger the damage at the centre o the FE model where the restraint was high. Material properties The material under investigation was an API X100 grade gas pipe (36 O.D 19mm W.T). The measured mechanical properties o the material and its chemical composition are set out in Tables 1 and. Table 1. X100 steel mechanical properties in transverse direction Young s modulus GPa Yield strength (0.% proo stress) MPa Tensile strength MPa Yield/UTS Table. X100 steel chemical composition reported by the pipe manuacturer element C Si Mn P S Cu Ni Cr Mo Nb Ti Al (wt%) The true stress-strain data required or FEA was obtained rom the tensile tests on plain bar specimens, see Fig stress (MPa) nominal stress-strain true stress-strain strain (mm/mm) FIGURE 1. Nominal and true stress-strain curves or X100 steel

3 Experimental work ECF15 Smooth and notched round tensile bars were taken rom the original pipe in the transverse orientation and tested on a servo-hydraulic Instron 8501 test machine with hydraulic grips under displacement control o 0.01mm/s. A transverse extensometer was used to capture the reduction o specimen diameter in each test. This was subsequently used or tuning the inite element damage model or lat racture. Three sets o laboratory specimens with dierent gauge diameter and notch acuity (i.e. dierent constraint levels at the gauge section o the test specimen) provided suicient data to study the ductile lat racture characteristics o X100 steel. The design dimensions o the tensile specimens are given in Table 3. Table 3. Speciications o notched tensile specimens tensile specimens number o gauge gauge notch notch R o specimens length diameter curvature diameter ρ (mm) (mm) ρ (mm) R o (mm) smooth notched 1 st set notched nd set Due to the rolling schedule o the pipe, the material was highly anisotropic. All tensile specimens suered considerable ovalisation. Fig. illustrates the deormed cross section o a plain tensile specimen with the minor and major axes in the pipe thickness and axial orientations, respectively. slant racture lat racture FIGURE. SEM o oval cross section rom plain bar tensile specimen The directional properties o the X100 steel led to dierent load-diametral contraction in the pipe thickness and axial directions as shown in Fig. 3.

4 load (kn) thickness direction axial direction diametral contraction in pipe thickness direction 15 diametral contraction in pipe axial direction diametral contraction (mm) FIGURE 3. Load-diametral contraction or plain par tensile specimen Finite element analysis The simulation o all test specimens was carried out using the modiied Gurson ductile damage theory [5,6] and the commercial inite element code ABAQUS 6. [7]. The Gurson yield potential is typically expressed as: σ Φ = ( σ eq Y ) + q 1 cosh( q 3p ) (1 + q σ Y 3 ) = 0 where σ eq is the von Mises equivalent stress, σ Y the material yield strength, p the hydrostatic pressure, q 1, q and q 3 are material constants, and is the damage parameter. The values o the q parameters are typically around q 1 = 1.5, q = 1.0 and q 3 = q 1 or erritic steels. In this model, racture propagates when the damage parameter reaches its critical value designated by c (threshold o rapid loss o stress carrying capacity). The damaged elements are removed rom the analysis simulating crack growth through the microstructure. The inal void volume raction at total ailure is represented by. These two, as well as q 1 and q, are considered as material constants. Thereore, in total, our constants should be determined to perorm the damage simulation. The initial void volume raction o X100 steel can be calculated rom Franklin s ormula [8]: o v = v ( d x d d 1 y ) z = 0.054( S% ) (3) Mn% where d x, d y and d z are the average dimensions o the inclusions. I a spherical inclusion shape is assumed, equation () gives o = v. From this an initial void volume raction 0 = was ound or this steel. (1) ()

5 Typical values o the q parameters were used to start the simulation. The critical and inal void volume raction was determined by a trial and error procedure until the model response matched the experimental data. Another important parameter in the model is the critical mesh size l c which is a representative o the average inter-particle distance. It is a representative o the average interparticle distance and is determined either by SEM study or rom the FE analysis. In this research the latter was used to ind the proper cell size. A value o l c = 00µm was ound to work well or all tested specimens. This was transerable to dierent numerical models. FE analysis showed that the damage theory was able to simulate the ailure behaviour o all test samples. Typical Gurson damage parameters or lat racture proved to be applicable to this high-strength low-alloy X100 steel. The values o the calibrated damage parameters are listed in Table 4. A small critical void volume raction c = (compared with a typical value o 0.15) was needed to trigger the damage at the centre o the FE model. Table 4. Damage modelling parameters used in FE analysis o lat racture q 1 q q 3 l c (mm) o c Results and discussion Fig. 4 shows the contour plots o void volume raction in a smooth tensile specimen beore the damage o the central elements. Due to high levels o stress triaxiality, the maximum cavity occurs in the centre o the specimen resulting in high values o void volume raction. When the void volume raction reaches its critical value, the central elements are ailed and removed rom the analysis. The ailure o subsequent elements occurs in the same manner simulating the progression o lat racture in the horizontal symmetry plane o the model. maximum void volume raction FIGURE 4. Contour plots o void volume raction in plain bar tensile model beore the ailure o the central elements

6 Fig. 5 is the results o the test and simulation on dierent tensile specimens smooth (test) smooth (simulation) notched, 1st set (test) notched, 1st set (simulation) notched, nd set (test) notched, nd set (simulation) load (kn) 40 0 change in racture mode B A C diametral contraction (mm) FIGURE 5. Load-diametral contraction rom smooth and notched tensile bars The comparison o the results o tests and numerical simulations shows good agreement in the sotening region except at the tail part o the plots. This shows that the micro-mechanical damage models calibrated on lat racture are transerable rom one set o test specimen to others with dierent restraints and geometry. The disagreement between the tests and FE models (starting rom points A, B and C in the load-diametral contraction diagrams) is a result o the racture mode transition rom lat to slant, see Fig. 6. The inal stage o crack propagation in tensile specimens is dominated by slant racture. Thereore, a dierent model is required to represent this ailure mechanism. slant racture lat racture point A FIGURE 6. Schematic o necking o smooth tensile bar (let) and cup-cone ormation(right) (point A is associated with the sudden load drop shown in plots o load-diametral contraction)

7 Fig. 6 shows the necking o a smooth tensile specimen and the subsequent shear racture propagation near its surace. The lat racture in the centre o the specimen is associated with a plane strain stress state. Near the ree surace o the specimen, the stress conditions are plane stress. This causes shear band ormation at the edges o the specimen resulting in a lat to slant racture transition. Consequently, a crack having either +45 or -45 degree (depending on which quarter o the specimen is being modelled) is ormed and propagates towards the specimen surace. The result is the cup and cone ormation on the racture surace o the broken specimen (see Fig. ). Fig. 7 is the distribution o shear stresses in the smooth tensile specimen shortly beore and ater the ailure o the central elements. The localisation o shear stresses at the edges o the specimen and the orientation o shear racture propagation can be observed in this diagram. maximum shear stress direction o shear racture propagation direction o lat racture propagation redistribution o shear stress in FE model FIGURE 7. Contour plots o shear stresses in plain bar tensile model beore (let) and their redistribution ater the ailure o central elements (right) The inormation on this lat-to-slant racture transition derived rom the FEA is given in Table 5. specimen point load P (kn) Table 5. Flat-to-slant racture transition data rom FE models P/P max diameter d (mm) d/ R o a mm lat racture energy ( J / mm ) shear stress (MPa) smooth bar A % % notched - 1 st set B % 5. 65% notched - nd set C 9.7 9% % σ m σ eq Fig. 8 shows the stress triaxiality data ( τ = σ m / σ eq, where σ m is the mean stress and σ eq the von Mises equivalent stress) in dierent sets o tensile bars at the onset o lat racture in the centre o the models and the onset o slant racture near their suraces. As can be seen, stress triaxiality is a linear progressing unction o the ratio o notch radius to notch curvature ( R o / ρ ). At the onset o lat racture, the stress triaxiality was maximum in the second sets o notched specimens with a sharp notch. At the onset o slant racture, stress triaxiality ahead o the crack tip in both sets o notched specimens had similar values. These were consistent with stress

8 triaxiality values o the smooth specimens. Interestingly, shear stresses ahead o the crack tip were similar in all tensile bars. This suggests that in tensile testing o this X100 steel, the transition rom lat to slant racture can be characterised by an average stress triaxiality value o the order o mean stress/mises stress smooth bar notched bar (1st set) notched bar (nd set) mean (0.88) best it onset o lat racture onset o slant racture ratio o notch raduis to notch curvature FIGURE 8. Comparison o stress triaxiality values in dierent sets o tensile specimens Fracture inormation presented in Table 5 gives an average value 1.0 ( J / mm ) or the energy consumption rate during the lat racture propagation in this steel. This agrees well with the value o 1.1 ( J / mm ) or the lat racture speciic energy in the same material measured on standard C(T) specimens [4], and with similar data reported by Stampl and Kolednik [9]. Conclusion The experimental data rom tensile bars used together with the damage mechanics theories was able to simulate the observed behaviour o tensile specimens made rom high-toughness pipeline steel o grade X100. An isotropic axi-symmetric model was able to simulate the mean load-diametral variation in the pipe thickness direction. Typical Gurson damage parameters or lat racture proved to be applicable to high-strength low-alloy X100 steel. However, a small critical void volume raction c = was needed to trigger the damage at the centre o the FE model where the stress triaxiality was high. An average value 0.88 o stress triaxiality was able to characterise the onset o the lat-to-slant racture transition in all tensile bars. Reerences 1. Demoonti, G., Mannucci, G., Spinelli, C. M., Barsanti, L. and Hillenbrand, H. G., In Proceedings o Pipeline Technology, edited by R. Denys, Elsevier Science, 000,

9 . Makino, H., Kubo, T., Shiwaku, T., Endo, S., Inoue, T., Kawaguchi, Y., Matsumoto, Y. and Machida, S., ISIJ International, Vol. 41, No. 4, 001, Leis, B. N., Eiber, R. J., Carlson, L. and Gilroy-Scott, A., In Proceedings o International Pipeline Conerence, Vol. II, ASME, 1998, Hashemi, S. H., Howard, I. C., and Yates, J. R., Submitted to ECF-15 or publication, Gurson, A. L., Journal o Engineering Materials and Technology, Vol. 99, 1977, Tvergaard, V., International Journal o Fracture Mechanics, Vol. 17, 1981, Hibbitt, H. D., Karlsson, B. I. and Sorensen, E. P., ABAQUS User s Manual (R. 6.), Franklin, A. G., J. Iron and Steel Inst., 07, 1969, Stampl, J. and Kolednik, O., Int. J. Fract., Vol. 101, 000,