YIELD STRENGTH AND FLOW STRESS MEASUREMENTS OF TUNGSTEN SINTER ALLOYS AT VERY HIGH STRAIN RATES

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1 YELD STRENGTH AND FLOW STRESS MEASUREMENTS OF TUNGSTEN SNTER ALLOYS AT VERY HGH STRAN RATES R. Tham, A. Stilp To cite this version: R. Tham, A. Stilp. YELD STRENGTH AND FLOW STRESS MEASUREMENTS OF TUNGSTEN SNTER ALLOYS AT VERY HGH STRAN RATES. Journal de Physique Colloques, 1988, 49 (C3), pp.c3-85-c3-90. < /jphyscol: >. <jpa > HAL d: jpa Submitted on 1 Jan 1988 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 JOURNAL DE PHYSQUE Colloque C3, Supplgment au n09, Tome 49, septembre 1988 YELD STRENGTH AND FLOW STRESS MEASUREMENTS OF TUNGSTEN SNTER ALLOYS AT VERY HGH STRAN RATES R. THAM and A.J. STLP ~raunhofer-nstitut fiir Kurzzeitdynarnik, Ernst-Mach-nstitut, Freiburg, F. R. G. Resume - Les experiences se font avec des barres en alliage fritte ayant une teneur de tungstbne superieure 3 90 %, sur lesquelles sont appliquees des jauges de contrainte. Plusieurs projectiles rigides en acier trempe sont projetks, 3 des vitesses differentes variant entre 100 et 400 m/s, sur les faces frontales des barres. Le phenomhne de deformation, suivit par les thoins, est enregistre B 'aide d'un enregistreur de transitoire h 200 MHz. Lors d'une vitesse de deformation de 3000 l/s, la limite dlastique des materiaux est trois fois superieure h la constante statique. En considerant le domaine plastique la forme de la courbe du diagramme contrainte/deformation n'est pas influencke par la vitesse de deformation, vu que la vitesse de propagation de l'onde de compression depend uniquement du degre de deformation. Abstract - Long rods of various tungsten sinter alloys with a tungsten content higher than 90 % were instrumented with strain gauges and struck by a moving anvil at velocities between 100 m/s and 400 m/s. The strain-time history at different locations on the rock surface was recorded by a 200 MHz transient recorder. The calculated yield stresses ranged at a level up to three times the static value, at a rate of s. n the plastic regime, the shape of the stress-strain curve remained unaffected by the strain rate, with a constant wave velocity for each strain level. 1 - NTRODUCTON There is only little knowledge of the behaviour of tungsten sinter alloys under dynamic loads. Conventional testing techniques, such as the servo-hydraulic testing machine, allow the study of the rate influence in a quasi-static regime up to a strain rate of s. At higher strain rates, beyond 102 l/s, a special experimental method was developed in order to determine elasto-plastic material properties up to a strain rate of lo4 11s. The theoretical basis of the investigations is given by the theory of von Karman 111, which was modified in order to take into account the rate dependence of the respective constitutive equations. 2 - EXPERMENTAL METHODS The materials under study were two-phase tungsten sinter alloys, having a tungsten content between 90.5 % and %. The matrix phase consisted of nickel and iron in a ratio of 7 : 3. n spite of the brittleness of the tungsten grains, these alloys behave in a ductile manner which is due to the ductile matrix, where crack propagation occurring under loading is 'stopped at grain-matrix interfaces. The reaction of these alloys under tensional loading was studied by means of a servohydraulic testing machine. Strain rates between s up to s were obtained. The sample was a standard tension-test specimen having a length of 40 mm and a diameter of 4 mm. Article published online by EDP Sciences and available at

3 C3-86 JOURNAL DE PHYSQUE The experimental set-up for compression tests at very high strain rates is given in fig. 1. strain gauges samp(e tngger 1 counter -.. projectiie velocity pins ~heaktbnc ditf. 200 MHz bridge ampl digitizer Fig. 1 - Experimental set-up for dynamic strain measurements. The method of the inverse impact was applied where a rigid projectile was fired against the stationary test rod by means of a compressed air gun. The rod with a diameter of 5.8 mm and a length-to-diameter ratio of 10 or 20, respectively, was held by a styrofoam cylinder. The impact site was polished and adjusted perpendicular to the launch tube's axis (better than 1 mrad). The mass of the impactor was 25 times the rod mass; thus inertia forces could be neglected and the rod was accelerated to the projectile's velocity. The velocity of the striker was measured by two velocity pins inside the barrel. t ranged between 100 m/s and 400 m/s. Strain measurements at the outer surface of the test rod were performed by means of strain gauges at distances between 15 and 35 mm from the front face. A special type of high elongation strain gauges with a length of 0.38 mm (Vishay Micromeasurements EP CF-120) have been used at a time resolution of better than 0.1 p s for elastic wave propagation. Each strain gauge was connected to a Wheatstone bridge circuit by means of 0.04 mm thick wires. Thus, lateral forces, acting on the gauges and the test rod during the acceleration, were negligible. The bridge was unbalanced by a resistance change of the gauge caused by the compression wave. After amplification the output voltage was recorded by means of a 200 MHz transient recorder. 3 - THEORETCAL ASPECTS Strain Calculation: Usually the resistance change of strain gauges is considered to be strictly proportional to the applied strain. The error due to this assumption is negligible for strains below 1 %, but becomes relevant at higher strain levels. With regard to this fact, a theoretical consideration relates the true strain with the resistance change of the gauges R by the formula where R denotes the nominal gauge resistance and k the gauge factor. A Taylor series of this expression, with a gauge factor of approximately k = 2, yields the experimentally established relation (2)

4 ~urth-rmore, the non-linearity of the bridge at higher strain levels was taken into account for the calculations. Calculations of stress: The theory of von Karmann /1/ is based on the solution of the strain rate independent relation 0 = o(e) between one-dimensional stress and strain. n this analysis, this assumption was replaced by a set of parametric functions a = "(') 2 =.const (31, whereby the rate dependence is taken into account. This results in a set of functions 'P 2 a = / P 0. ( 1 d~ 1 i ; const (4) with constant rate where P denotes the material density, C(E) the wave velocity (dependent on the strain level) and E pl is the maximum plastic strain. A separation of the elastic and plastic part yields where co is the elastic wave speed, Eel the maximum elastic strain and cpl (!) the velocity of the plastic wave at a given strain rate. This relation allows the calculation of the stress, provided that the plastic wave velocity corresponding to each strain level is determined at several locations from the impact site. 4 - RESULTS n the quasi-static regime three alloys with densities of 17, 17.6 and 18.5 g/cm3 (D 17, D 17.6, D 18.5(1)) have been investigated under one-dimensional tension loading. Since all three alloys show a similar behaviour, the stress-strain diagram for D 18.5 is given in fig. 2, representatively. Fig. 2 - Quasi-static stress-strain relations for D 18.5 at 20 OC. =met (brand name)

5 C3-88 JOURNAL DE PHYSQUE The yield strength is increasing from 558 MPa at a strain rate of 11s to 760 MPa at s. Correspondingly, the UTS increases from 738 to 845 MPa while the elongation is reduced from 7.2 % to 3.9 %. The strain rate sensitivity is smaller when the static material strength is increased by a thermo-mechanical treatment, as in the case of the alloy D Here only the elongation reduces to about 50 % when the rate increases from 10-4 l/s to 10- l/s, while strength values are not affected. The strain measurements from dynamic compression tests result in strain-time curves of the type shown in fig AU F- - \ O c - C.S~C )P.*~c - 1% W - D 18.5 L L.,= 58mm.LO z 0 Lo= 58mm,L/O=O 2%. u = ll8mlr gmugr ~ocat~on S mm, 3W u = 118mls gauge ~ocatoon 250mrn l BL 6L L L ty51-1 ps1 6 Fig. 3 - Compression wave profiles at two distances from the impact site. These curves were recorded on a D 18.5 test rod, which was struck by a projectile at a velocity of 148 m/s. The gauge location was 15.1 mm and 25.0 mm, respectively. When the compression waves reaches the gauge, the strain rises nearly linearly up to the elastic limit strain. At the transition to plastic behaviour the strain rate drops to very low values and then increases again. The much faster elastic wave is reflected as a tension wave at the free end of the rod. t interferes with the incident plastic compression wave. Weak plastic compression stresses are reduced below the elastic limit, and a new elastic compression wave is generated. Therefore, the record at 25 mm gauge location shows two reflections at 19.6 us and 38.2 us. An interpretation of the curves beyond the first interference of the waves cannot be given. To avoid this effect, rods with a length-to-diameter ratio of 20 were used. Depending on the impact velocity and the gauge location, plastic strains up to 15 % and strain rates up to 1.3 x s have been measured. The experiments proved that, within the accuracy of the method, an elastic disturbance propagates at a sound velocity defined by the equation co = (E = Young's modulus; p = material density). co is not affected by the elastic strain rate which, in these experiments, ranged between s and s. The elastic limit strain increases with increasing strain rate. By the determination of the strain, when the material starts to behave plastically, the rate dependent yield stress was calculalted using equation (5). The result is shown in fig. 4.

6 Fig. 4 - Strain rate dependence of the yield stress for three W-sinter alloys. Under comparable impact conditions, the obtained strain rates for the material D 17 were inferior to those of D 17.6 and D This may be due to the higher strength of the latter material. Furthermore, the elastic-plastic transition in the strain-time curve of D 17 was less well defined than for the other alloys. t resulted in a considerable error within the calculation of the yield strength. The experiments demonstrate that the plastic wave velocity was not influenced by the strain rate, which ranged between s and s. For D 18.5 the speed of the compression wave is given as a function of strain in fig. 5. eps C p l ) [% Fig. 5 - Rate-independent plastic wave velocity as a function of plastic strain (material D 18.5) t rapidly drops from the elastic value to a nearly constant wave velocity (- 460 m/s) at strains beyond 10 %. Using the equation (5) the stress-strain-diagram was established for strain rates ranging form 1500 l/s to s (fig. 6).

7 JOURNAL DE PHYSQUE B * N r n \ r n STRAN C%l m : :! : Fig. 6 - Stress-strain relation under compression at four strain rates (material D 18.5). 5 - CONCLUSONS t was found that the strain rate in dynamic compression experiments affects only the elasto-plastic transition point but not the further plastic behaviour of the sinter alloys investigated. For strain rates between 10-4 l/s and s the deformation mechanism of high density W-sinter alloys can be explained by the theory of thermal activation of dislocations, where the flow stress varies linearly with the logarithm of the strain rate. The steep increase of the yield strength, proportional to the strain rate, with values above lo3 l/s, implies that dislocation drag mechanisms are mainly responsible for the compression behaviour of W-sinter alloys. REFERENCES // von Karman, T. and Duwez, P., 3. of Appl. Physics 21 (1950) 987. /2/ Hoffmann, K., "Kennlinienverlauf von DehnungsmeOstreifen bei deren Anwendung im Hochdehnungsbereich", Druckschrift der Hottinger Baldwin MeOtechnik GmbH