Comparison of grain size and strain rate influences on higher temperature metal strength and fracturing properties

Abstract

A review is given in honor of David Taplin’s researches, with colleagues and students, on grain size aspects of the higher temperature plastic deformation and failure behaviors of metals and alloys. Comparison is made with lower temperature grain size strengthening measurements and their Hall–Petch (H–P) dislocation pile-up model description. One focus is on H–P prediction of the true fracture strain dependence on grain size or particle spacing. The second focus is on the relationship between the thermal activation based Zerilli–Armstrong (Z–A) relations for fcc or bcc metal strength levels and the historical Zener–Hollomon (Z–H) and Larson–Miller (L–M) parameters employed to describe the combination of higher temperature and lower strain rate, or creep type, results. Particular measurements are reviewed for copper, magnesium, copper-nickel Monel alloy, titanium, nickel, aluminum alloy and ferritic and austenitic steel materials.

Keywords

Grain size strain rate Hall-Petch relations strength fracturing

1. Introduction

David Taplin was first met at the Department of Mining and Metallurgy, University of Melbourne, Australia, in 1964. He was, together with Professor R.C. Gifkins and students and colleagues, pursuing research on the influence of grain size on the higher temperature fracturing properties of polycrystalline OFHC copper [1,2]. Earlier work had been with V.N. Whittaker on comparison of creep ductility results obtained on a two-phase Al-Mn alloy and on 𝛼-brass [3,4]. Opposite influences of grain size reduction either decreasing or increasing the creep ductility were measured, respectively, at 723 K and very notably, the positive grain size effect in 𝛼-brass was associated with a similar grain size influence on the ductile fracture stress. The discussion article with Gifkins on cavity growth mechanisms [1] and other experimental observations made with Fleck and Cocks [2] were importantly included in a review done by Perry [5]. Later acquaintance with David was at ICF2 in Brighton, UK, where his long term commitment to the International Conferences on Fracture was initiated. Subsequent personal interactions were at ICF3 in Munich, Germany, and at ICF4 in Waterloo, CA, USA. David Taplin’s official commitment to the management and very significant growth internationally of ICF has continued through the twelve quadrennial meetings until his retirement at ICF14.

The current article is dedicated to David by starting from our early research interaction on the fore-mentioned grain size aspects of both lower and higher temperature metal fracturing. An updated review and analysis are provided of research understanding on the higher temperature aspects of the topic. The report builds onto earlier investigations of the present author concerning lower versus higher temperature grain size dependencies of strength which had been presented at the 1967 Battelle Dislocation Dynamics Meeting [6] and at the 1970 16th Sagamore Army Materials Research Conference [7]. The referenced reports presaged broader employment of the extended Hall–Petch (H–P) relation described in [8] as $\begin{eqnarray}\displaystyle {\sigma}_{{\varepsilon}}={\sigma}_{0{\varepsilon}}+k_{{\varepsilon}}\ell ^{-1/2}. & & \displaystyle\end{eqnarray}$ (1)

In equation (1), 𝜎_𝜀 is the true stress at true strain 𝜀, 𝜎_0𝜀 is friction stress, k_𝜀 is microstructural stress intensity, and ℓ is average grain diameter. The value of 𝜀 may be the initial yield strain or proof strain determined for yielding or the subsequent strain for a plastic flow stress that is finally terminated in fracturing [9]. Figure 1 shows such H–P type example applied for a compilation of the ambient temperature true fracture strain, 𝜀_f, dependencies on ℓ^−1∕2 of magnesium materials [10], including addition of more recent measurements of compressive strain rate influence shown for the open and closed triangle points at ℓ = 10 microns [11]. For the inset equation, 𝛥k = k_f − k_y, is the difference in microstructural stress intensities for the true fracture stress, 𝜎_f, and yield stress, 𝜎_y, and h is the average true strain hardening coefficient, generally taken to be independent of grain size. In like manner, 𝜀₀ = 𝜀_f −𝜀_y. More is to be shown later in presentation of 𝜀_f measurements for the low temperature deformation of Armco iron and creep of copper as well as in description of higher temperature grain size dependent deformation results reported for magnesium.

Fig. 1.

True tensile fracture strain, 𝜀_f, dependence on reciprocal square root of average grain diameter, ℓ^−1∕2, for polycrystal magnesium materials spanning a range in grain size [9,10].

2. Grain size weakening at higher temperature

Historical concern with a transition from expected grain size strengthening to weakening began with Jeffries [12] who defined an ‘equicohesive temperature’ as the point where the changeover would occur. Very interestingly, Mathewson provided a discussion of the extensive measurements given by Jeffries on material ductility for which doubt was expressed that a proposed increase in ductility was to be achieved for smaller grain size material [13]. Mathewson made reference also in his discussion to recent measurements reported at the time of an increased hardness being obtained for smaller grain size cartridge brass material, which results Jindal and Armstrong showed much later in a compilation of related hardness measurements to follow closely an H–P dependence [14]. Crussard and Tamhankar [15] gave a comprehensive description of the equicohesive temperature behaviors measured for Armco iron and nickel-chromium steel materials. Modern application of the concept has been reported by Nganbe and Fahim [16] for measurements made on powder-consolidated nickel-based superalloy material.

Kutumba Rao, Taplin and Rama Rao had reported a reversed H–P behavior at 973 K and higher temperature, T, for chromium manganese nitrogen stainless steel material showing conventional grain size strengthening at 300 K [17]; see also Kutumba Rao and Rama Rao [18]. Other examples of the transition from grain size strengthening to weakening behavior at higher temperatures are shown in Fig. 2 for a compilation of selected measurements from more extensive results reported over a range of grain size in each case of the steady state creep rate, $\acute{{\varepsilon}}_{S}$ , determined for copper, chromium-nickel stainless steel and Monel materials [19]. Connection of the grain size dependence of Monel with Astroloy superalloy material behavior had formed the Ph.D. thesis work of E.K. Weaver [20]. Comparison of grain size strengthening and weakening behaviors was reported by Mannan and Rodriguez [21] for 316 stainless steel material tested at 873 and 973 K, and followed similarly by Ray, Samuel, Mannan and Rodriguez [22] for the same material tested at 1123 K. More recent results have been reported for BFe10-1-2 cupronickel alloy by Cai et al. [23] and involving match with constitutive relation prediction. Armstrong had suggested that advantage could be taken of processing weaker fine grain size material at higher temperature and then utilizing the product which would be stronger in lower temperature application [7].

Fig. 2.

Grain size dependence of the steady state creep rate, $\acute{{\varepsilon}}_{S}$ , demonstrating higher temperature grain size strengthening and/or weakening over a range of grain size [19].

3. H–P and thermal activation – strain rate analysis (TASRA) relations

At the time of Hall [24] and Petch [25] reporting their development of what came to be known as the H–P relations for the yield and cleavage stresses of iron and steel materials, Carreker and Hibbard were reporting comprehensive measurements on the temperature, strain rate and grain size dependence of the stress-strain behavior of high-purity copper [26]. Armstrong compared the reported temperature-dependent (proof) yield stress measurements with single crystal critical resolved shear stress measurements in demonstration of cross-slip being responsible for determining the value of the H–P k_𝜀 [27]. A similar comparison between polycrystal and single crystal measurements was made for the analogous correlation of strain rate dependencies. At T > ∼1000 K, the value of k_𝜀 indicated in the Carreker and Hibbard results was almost too small to measure [6] but the indication in Fig. 2 at 773 K is for a finite value estimated as ∼1.0 MPa mm^1∕2, which value is noted to be a typical k_𝜀 magnitude for the grain size dependence of high-purity aluminum at ambient temperature. The value compares with k_𝜀 = ∼5 MPa mm^1∕2 for copper at ambient temperature which value is about the same as measured for nickel material and explained on a dislocation pile-up model basis in terms of comparable products obtained for the two materials of their shear modulus and single crystal cross-slip stress [28]. Blum and Zeng [29] and Blum et al. [30] have published more recent results on comparable strain rate sensitivity measurements made for ultrafine-grained copper and nickel materials.

Fig. 3.

The yield stress of titanium (and Ti6Al4V) materials accounted for by Zerilli and Armstrong [35] in a temperature-compensated strain rate dependence description after the method of Zener and Hollomon [34]; the solid-triangle points are added for high rate tensile split-Hopkinson pressure bar measurements of Mocko, Kruszka and Brodecki [36].

There is a long history of researches on development of constitutive relations for the higher temperature deformation of metals and alloys and often with consideration given to the influence of grain size. Blum, Li, Zhang and Weng [31] have dealt presumably with temperatures below the grain size dependent strengthening/weakening transition and therefore retained an H–P type dependence on grain size. Schneibel et al. have presented temperature-dependent flow stress results indicating changeover only at very high temperature for very small grain size material; see their Fig. 9 [32]. Otherwise, Blum et al. and most other researchers have employed a coupled temperature/strain rate dependence that follows naturally for a thermal activation – strain rate analysis (TASRA) type dislocation mechanics description following on, though more complicated [33], from the original thermal activation description [34] given by Zener and Hollomon (Z–H). Zerilli and Armstrong [35] have employed a TASRA description in their own Z–A constitutive equation development for the temperature and strain rate dependencies reported, for example, for measurements on titanium (and Ti6Al4V) materials as shown in Fig. 3. Several new measurements recently reported by Mocko et al. [36] for high loading rate split-Hopkinson tensile tests have been added to the figure whose scale extends to a higher temperature region where the strain ageing ‘bump’ is observed near to the abscissa axis.

The Z–A description follows from a thermal activation – strain rate analysis (TASRA) type relationship for strain rate, $\acute{{\varepsilon}}_{S}$ , expressed in an initial form [37,38] $\begin{eqnarray}\displaystyle \acute{{\varepsilon}}=\acute{{\varepsilon}}_{0}\exp \left[-\left(G_{0}-\int v^{\ast }d{\tau}_{Th}\right)/kT\right]. & & \displaystyle\end{eqnarray}$ (2)

In equation (2), $\acute{{\varepsilon}}_{0}$ is a reference strain rate; G₀ is the Gibbs free energy of activation; v^∗ = A^∗b, is the activation volume that is determined by the product of activation area, A^∗, times b, the dislocation Burgers vector; 𝜏_Th is the thermal component of the applied shear stress; and, k is Boltzmann’s constant. It may be seen with substitution of $G\{{\tau}_{Th}\}=[G_{0}-\int v^{\ast }d{\tau}_{Th}]$ in equation (2), then $\begin{eqnarray}\displaystyle G\{{\tau}_{Th}\}/k=T\ln (\acute{{\varepsilon}}_{0}/\acute{{\varepsilon}}). & & \displaystyle\end{eqnarray}$ (3)

On such basis, equation (3) accounts for the temperature-compensated strain rate parameter appearing in the abscissa scale of Fig. 3. The parameter was first put forward by Zener and Hollomon [34]. The value of 𝜏_Th in equation (2) is determined, in turn, by the relationship $\begin{eqnarray}\displaystyle {\tau}_{Th}=(1/m)[{\sigma}_{{\varepsilon}}-{\sigma}_{G}-k_{{\varepsilon}}\ell ^{-1/2}]. & & \displaystyle\end{eqnarray}$ (4)

In equation (4), m is a Taylor orientation factor and 𝜎_G = m𝜏_G is an athermal stress dependent on the dislocation density and solute content. Following the Z–A development, a reciprocal dependence of v^∗ on 𝜏_Th, that is v^∗ = W₀∕𝜏_Th, allows transformation of equation (2) into a form to be made use of in the following account: $\begin{eqnarray}\displaystyle \acute{{\varepsilon}}=\acute{{\varepsilon}}_{0}\exp [-G_{0}/kT]({\tau}_{Th}/{\tau}_{Th0})^{w0/kT}. & & \displaystyle\end{eqnarray}$ (5)

The reciprocal dependence of v^∗ on 𝜏_Th is shown in Fig. 4 that is now updated to include a number of dashed line, creep-type, measurements made on ferritic and austenitic steel materials at higher temperatures. The top-most dashed line for measurements reported at 1298 K is contained within the width of the two lower dependencies determined, on the left side, at 1500 and on the right side, at 857 K [39]. These measurements and many others compiled for a number of metals, alloys, semiconductors and ionic solids, as reported by Balasubramanian and Li, were extended to include likewise, and very importantly, grain boundary sliding measurements reported for copper between the temperatures of 773 and 1159 K [40].

Fig. 4.

Compiled measurements of v^∗ = A^∗b for combined shock, stress-strain, and creep tests.

Despite the similar dependencies of the v^∗−𝜏_Th relationship for conventional and creep test measurements, recognition has to be given to an alternative constitutive relationship more often employed to describe higher temperature deformations, particularly involving steady state creep deformation at constant stress, 𝜎, and normally written for a creep rate controlled by grain boundary sliding occurring through action of an appropriate diffusion mechanism as [41] $\begin{eqnarray}\displaystyle \acute{{\varepsilon}}_{S}=(AD_{L}Gb/kT)(b/\ell )^{p}({\sigma}/G)^{q}. & & \displaystyle\end{eqnarray}$ (6)

In equation (6), A is an experimental constant, D_L is a relevant diffusion coefficient with its own activation energy, G is shear modulus, and the exponents, p and q, are constants usually equal to 1 or 2. It may be seen that equation (6) leads to a reverse H–P dependence at constant value of $\acute{{\varepsilon}}_{S}$ . Local grain boundary shearing by a diffusion-based mechanism is taken to be rate controlling with presumption of the diffusion being stress-driven via a number of different mechanisms [42]. Important accounts of such different mechanisms have been given by Mukherjee [43] and by Padmanabhan [44]. Padmanabhan made connection of the constitutive relation with superplastic deformation. And coincidentally, Chapman and Wilson [45] attributed the higher 𝜀_f values in Fig. 1 to occurrence of superplasticity. Reference [46] provides a compilation of lattice diffusion coefficients and activation energies for a wide range of metals. Values of v^∗ determined from equation (2) and equation (6) for different nano-scale grain size regions have been reported for zinc [28] and copper [47,48] materials.

4. Creep of copper and its ductility

Nabarro had developed a creep deformation map delineating stress and grain size regions of different operating mechanisms for copper, aluminum and related metals [49]. Figure 5 shows a version of the map for copper including estimation of the operating ranges in grain sizes and stresses [50]. The H–P based copper result shown in Fig. 2 at a stress level of ∼50 MPa and average grain diameter in the range ∼0.04 ≥ ℓ ≥ ∼0.02 mm corresponds in Fig. 5 (at that same stress level) to a limiting (small) grain size of ∼0.01 mm being on the H–P line. With an estimation of k_𝜀 = ∼1.0 MPa mm^1∕2 at T = 773 K, as determined from the pioneering Carreker and Hibbard results [6,26], a value of v^∗ = ∼2.1 ×10⁻¹⁸ mm³ is calculated from the H–P prediction of grain size dependence in Fig. 2. With 𝜎_o𝜀 = ∼30 MPa for the Carreker and Hibbard H–P dependence, as determined in reference [6], a value of 𝜏_Th = ∼10 MPa would put the corresponding v^∗ value reasonably close to the reciprocal dependence on 𝜏_Th shown in Fig. 4.

Fig. 5.

A theoretical creep deformation map for copper including deformation mechanisms: N–H for Nabarro–Herring, H-D for Harper–Dorn, P-L for Power Law, and H–P for a limiting Hall–Petch dependence; 𝜇 = G, for shear modulus, and d = ℓ, for average grain diameter [49,50].

In [2], Fleck et al. found for the intergranular cavitation of OFHC copper, at first, an increase in ductility with increase in grain size, then to be followed by a decrease in ductility at larger grain size. The reversal compares with the 1919 disagreement between Jeffries and Mathewson on the effect of grain size on ductility [12,13]. The Fleck et al. result was established both for reduction in area at fracture and for the total elongation. Very importantly, the full ductility behavior was correlated with description of two different fracture surface morphologies: first for the larger grain size material, on linking up of intergranular cracks associated with a (Griffith-Irwin) critical stress intensity condition, then transitioning at smaller grain size to a ‘void-sheet’ process with emphasis on a ductile hole-joining mechanism dependent on the volume fraction of voids. Fleck and Taplin had followed up the work with determination of both grain size strengthening and weakening measurements for a copper base dispersion alloy, Coronze [51]. Hall–Petch type grain size strengthening was established at ambient temperature for hardness results leading to the present estimation of a value of k_𝜀 = ∼8 MPa mm^1∕2. In creep tests at 673 K, the material was shown to give a minimum creep rate increasing at first with increase in grain size and then reversing itself.

Fig. 6.

Compiled results for grain size dependence of ductile fracturing of Armco iron [53] and spheroidized steel [55] and creep fracturing of OFHC copper [2].

The reduction in area measurements reported for the different grain size copper material in [2] provides a basis for determining the true fracture strains, 𝜀_f, at different grain sizes and comparison then with the positive type of H–P description given for magnesium in Fig. 1. Figure 6 shows such comparison also with iron and steel results for which a reversal in 𝜀_f has also been described [52]. The positive H–P based improvement in ductility for Armco iron on the left side of Fig. 6, relating to the magnesium measurements, was reported by Srinivas et al. [53]. There is addition on the ordinate axis of 𝜀₀ = (𝜀_0f − 𝜀_0y) as demonstrated, for example, for mild steel H–P results including yield, flow and fracture stress measurements [54]. The right side decrease in 𝜀_f was obtained from pioneering ductile fracture measurements reported by Liu and Gurland [55] for spheroidized steel materials of differing carbon contents. The curve through the measurements was predicted by Petch and Armstrong [56] for grain size dependent linkage of ductile hole-forming cavities. Zerilli and Armstrong [57] had added other measurements in a broader analysis. The highest value of 𝜀_f for the Liu and Gurland spheroidized steel material was measured for a lowest 0.065 carbon concentration. Das, Samanta and Chattopadhyay have reported reduced elongations for ultrafine-grained copper materials [58]. Schneibel and Heilmaier have given an analysis of Hall–Petch breakdown based on strengthening being controlled by a critical particle size and becoming more important at ultrafine grain size [59].

5. Constitutive relations/applications

The lower 𝜀_f values shown in Fig. 6 for creep fracturing of copper compared to the tensile fracturing of steel point to engineering concern with determination of the creep failure lifetime that is taken to be largely determined by the rate of steady state deformation occurring often at a miniscule strain rate. And nevertheless, the overall creep rupturing strains are normally small as shown in the figure. The Zener–Hollomon (Z–H) and Larson–Miller (L–M) relations are often employed to characterize such slow deformation rates. Connection is made here with extension of the Z–A relations to describe the same type behaviors, particularly as a number of recent investigations have employed the Z–A description to describe higher temperature material behaviors [60–64].

As noted in Section 3, there is close connection of the Z–H and Z–A relations because of both derivations being based on thermally-activated plastic flow. The Z–H parameter for the steady state creep rate, $\acute{{\varepsilon}}_{S}$ , is obtained from equation (3) as $\begin{eqnarray}\displaystyle \text{Z}{-}\text{H}=\acute{{\varepsilon}}_{0S}=\acute{{\varepsilon}}_{S}\exp [G\{{\tau}_{Th}\}/kT]. & & \displaystyle\end{eqnarray}$ (7)

In [65], the Z–H parameter determined for friction stir processing of magnesium AZ31B material was shown to increase with decrease in average grain diameter because of dynamic recrystallization occurring during deformation. Agreement was shown with other results reported for extruded as well as for annealed material. With incorporation of the v^∗−𝜏_Th dependence into equation (7), the Z–H parameter is obtained as $\begin{eqnarray}\displaystyle \text{Z}{-}\text{H}=\acute{{\varepsilon}}_{S}\exp [G_{0}/kT]({\tau}_{Th}/{\tau}_{Th0})^{-W0/kT}. & & \displaystyle\end{eqnarray}$ (8)

Application to the results reported in [65], with substitution of equation (4) for 𝜏_Th into equation (8), would correspond to grain size strengthening being operative in the material production. Other current measurements correlated with stress-dependent Z–H determinations have been reported for AZ41M magnesium alloy [66], nuclear reactor Alloy 617 [67], and nickel-based superalloy material [68].

Dieter [69] has given a useful description of using short time creep testing in order to predict long time failure results, particularly via the pioneering analysis put forward by Larson and Miller [70] to couple time to failure, 𝛥t, and temperature, T, in the eponymous Larson–Miller (L–M) parameter, $P\{{\sigma}\}$ , expressed as [69]: $\begin{eqnarray}\displaystyle \text{L}{-}\text{M}=P\{{\sigma}\}=T[\log {\Delta}t+C_{1}]. & & \displaystyle\end{eqnarray}$ (9)

In equation (9), T was expressed in units of Rankine temperature, °R = °F +460; and C₁ was taken as a constant with value of ∼20. Dieter provides an example ‘master plot’ of decreasing log 𝜎 vs. increasing P for Astroloy material, including measurements made over a range of 1400 to 1800 °F; see Figs 13–20. With substitution of (1∕𝛥t) for $\acute{\varepsilon}$ in equation (5), the result is obtained $\begin{eqnarray}\displaystyle (1/k)[G_{0}-W_{0}\ln ({\tau}_{Th}/{\tau}_{Th0})]=T[\ln {\Delta}t-\ln {\Delta}t_{0}]. & & \displaystyle\end{eqnarray}$ (10)

Comparison of the foregoing equations provides a basis for understanding the stress-dependent ordinate scale of a Larson–Miller plot. In their pioneering analysis, Larson and Miller obtained reasonably straight line dependences with negative slope of log 𝜎 vs. T[log 𝛥t +20] for low-carbon steel, C-Mo steel and 18-8 stainless steel materials. Larson and Miller gave a theoretical estimation of 𝛥t₀ having a value of ∼2.8 × 10⁻²¹ h, thus giving C₁ = ∼21.5. In supporting discussion, Fisher and Hollomon [71] were concerned with possible variation in C₁. With conversion of units, the L–M experimental slope values of the linear dependencies are found to vary between (−2.0 and −5.5) × 10⁻⁴ K⁻¹. Based on equation (10), the slope is given as (k∕W₀) = −4.5 ×10⁻⁴ K⁻¹, as obtained from the estimated linear v^∗ vs. 𝜏_Th dependence giving W₀ = 3.1 ×10⁻²⁰ J in Fig. 4. A slope of ∼−3.4 × 10⁻⁴ K⁻¹ is estimated for heat-resistant steels from summarized measurements reported by Tamura et al. [72], and slope of ∼−4.3 × 10⁻⁴ K⁻¹ for Waspaloy (superalloy) material by Yao, Zhang and Dong [73]. Also in accompanying discussion of the Larson and Miller article, Grant expressed concern for interference of oxidation on the long-time creep or stress rupture properties [74]. An example was provided for Monel material of a somewhat curved L–M dependence that is now an accepted observation. Antolovich has recently provided for superalloy materials a comprehensive fatigue property description in which the role of oxidation is included [75]. Kucher and Prikhod’ko have given a comparison of predictions obtained for the L–M and other parametric relations [76].

Taplin and Taylor provided a review of colleague work on creep properties of Inconel Alloy N-750 under partial vacuum conditions and of carburization effect on austenitic superalloy 800H [77]. Recently Abe has given a comprehensive description of creep behavior and lifetime measurements for Mod.9Cr-1Mo steel material including detailed Larson–Miller type measurements [78]. Other connection has involved comparison of Z–A and numerically-based Johnson-Cook constitutive models to predict elevated temperature flow behavior of modified 9Cr-1Mo steel [79] and likewise for both modified 9Cr-1Mo and alloy D9 behaviors [80].

Special note should be made of the referenced use of such constitutive equations in metal and alloy processing applications, relating to the early suggestion [6] of taking advantage of grain size weakening at elevated temperature for facilitating material processing, then to have a stronger material product at a lower design temperature. Osakada has provided a wonderful history of metal forming researches [81]. In more recent researches, Prasad and Rogers had reported on microstructural changes and plastic anisotropy in the strip drawing of copper [82] which led Prasad and colleagues onto the concept of deriving material processing maps [83,84]. Recent reports have dealt with processing maps for Al-Mg-Si alloy [85] and low-carbon steel [86] materials. Tekoğlu, Hutchinson and Pardoen have provided a continuum mechanics description of ductile void nucleation growth and coalescence [87]. Farabi, Zarei-Hanzaki and Abedi [64] employed a Z–A equation description in evaluating the high temperature formability of their dual phase brass material, thus relating also to the two-phase (Al-Mn alloy) deformation consideration raised by Taplin and Whittaker [3].

6. Grain size strengthening/weakening in magnesium

Pioneering results on creep of magnesium single crystals were reported by Conrad and Robertson [88] fore-shadowing Conrad’s extensive reporting on thermally activated dislocation motion in a great variety of materials, including single crystal [89] and polycrystal [90] copper materials. Also, Conrad had given his own TASRA-based description for the creep-determined stress-rupture properties of Nimonic alloy material [91].

Texture is a relatively important factor in determining both low temperature and higher temperature creep deformation properties of magnesium and other hexagonal close-packed metal structures. Hutchinson [92] produced a pioneering model description of the behavior in terms of different relative slip system ratios and applied the results to power law creep, including description of measurements on ice materials. Early H–P results on random orientation polycrystal magnesium were reported by Hauser, Landon and Dorn [93] and were coupled with metallographic observations of prism slip observations being made in the grain boundary regions [94]. Armstrong [95] employed the measurements to establish correlation of the temperature-dependent H–P 𝜎_{0 y} with basal slip and of k_y with prism slip. Wilson and Chapman [96] had reported H–P results on textured material, particularly on extruded material in which alignment with the extrusion direction of the basal slip direction and slip plane produced more active prism slip within the grain volumes with consequent increase in 𝜎_O𝜀 and decrease in k_𝜀. Excellent correlation of 𝜎_0𝜀 and k_𝜀 measurements with texture of magnesium and Mg-12.5 Li, Mg-5 Ti and Mg-12.7 Cd alloy materials formed the Ph.D. thesis of Sambasiva Rao [97]. Detailed measurements were reported for single crystal/polycrystal magnesium [98] and Mg-12,7 Cd alloy [99]. Recently, Armstrong employed a ratio of prism slip to basal slip shear stresses in evaluation of low temperature grain size dependent H–P results obtained on wrought magnesium material [52]. Grain size weakening measurements have been reported recently also for the high-temperature deformation of pure magnesium material by Cepeda-Jiminez, Molina-Aldareguia, Carreno and Perez-Prado [100], and by Somekawa and Mukai [101].

Recent research activity has been concentrated on Mg-3Al-1Zn (AZ31) alloy material. Barnett, Keshavarz, Beer and Atwell [102] have reported detailed H–P assessment of grain size dependent deformation twinning and slip behavior for extruded material tested at ambient temperature, 373, 423, and 473 K, also including evaluation of grain size influence on the Z–H parameter. Deformation twinning was concluded to be responsible for a larger k_.002 =9.5 MPa mm^1∕2 measurement at larger grain size, very near to the value obtained for the texture-free Hauser, Landon and Dorn material [93,94]. Transition to smaller k_y values of 2.5 and 0.73 MPa mm^1∕2 occurred for slip-dominated flow at 423 and 473 K, respectively. And very importantly, a transition was shown to occur from grain size strengthening to apparent grain size weakening at larger 𝜀 = 0.20 in a compilation of stress-strain curves depicted at the two higher temperatures. The grain size weakening stress-strain results appear to be in line with the historical measurements reported by Crussard and Tamhankar for an austenitic steel material tested at 973 K; see Fig. 2b in [15]. Gzyl, Rosochowski, Boczkal and Qarni have drawn specific comparison of the important result with their own measurements on equal-channel angular pressing (ECAP) of related AZ31B magnesium alloy [103]. Also, Gzyl et al. employed the Z–H parameter to characterize the processing characteristics of their material in comparison with other fracturing results obtained from the literature. A decrease in the Z–H parameter occurred with increasing initial grain size of the material to be processed. Other high-temperature creep test results have been reported for AZ31 material by Roodposhti, Sarkar and Linga Murty also employing the Z–H parameter to characterize the material deformation behavior involving dynamic recrystallization and grain boundary sliding [104]. Scanning electron microscope (SEM) observations were reported of increased intergranular fracturing at larger grain size as compared with more dimple-shaped fracturing at smaller grain sizes, in line with the pioneering observations of Fleck, Cocks and Taplin [2].

7. Summary

An account has been given of David Taplin’s early researches on creep fracturing which took place at about the same time that the International Conference on Fracture (ICF) was being formulated by Takeo Yokobori and by other international experts on fracturing. David’s principal concern with fracturing of metals and alloys connected immediately with the development of ICF to which he has made an outstanding commitment, as personally witnessed by the present author through several of the early ICF meetings, and is documented for all other ICFs since. The early research connection between us, as has been made evident in the current report, was on the influence of grain size on the deformation and fracturing properties of polycrystal metals and alloys. Such shared interest has led to the present description given of further developments on the topic which seems to have become more important over the intervening years, and particularly so because of advanced methods of material processing leading to grain size refinement down to nano-scale dimensions. Two topics given special attention in the present account are: (1) influence of grain size on creep ductility and fracturing; and (2) use of constitutive relationships in understanding/predicting metal and alloy deformation behaviors at relatively higher temperatures, as involved also in material processing methods.

Footnotes

Acknowledgements

It is a great pleasure for the author to thank his colleague, David Taplin, for encouragement to produce the present article. A much appreciated sabbatical leave from the Westinghouse Research Laboratory during 1964 and spent at the Commonwealth Scientific and Industrial Research Organization (CSIRO), Division of Tribophysics, Melbourne, Australia, provided the opportunity of first meeting David at the University of Melbourne.

Conflict of interest

None to report.

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