Analyses have been made on the sintering residual stress and the microscopic stress/strain under uniaxial tension in WC-Co hardmetal with a mechanical model of two-phase sintered materials, as proposed in a previous paper. The cooling process in sintering was simulated by introducing thermal stress into the mechanical model. The results obtained on the sintering residual stress in WC-grain and Co-binder agree well with the experimental values obtained by the X-ray diffraction method given in a reference. The analyses of the microscopic stress/strain in WC-grain and Co-binder were made under two initial conditions ; one with no sintering residual stress and the other with sintering residual stress. The results of the calculation have shown that the sintering residual stress has no influence on the maximum values of microscopic stress in the WC-grain and Co-binder, but it has influence on the plastic deformation in the Co-binder. The variation of the transverse rupture strength of WC-Co hardmetal, as a function of Co volume fraction V_Co, is explained based on two kinds of fracture criteria, one of which is effective, depending on the value of V_Co ; the transverse rupture strength is controlled by flaw size in the lower V_Co region, and by microscopic stress/strain in the higher V_Co region.

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The strain gage called "K-gage" was developed to measure the stress intensity factor (K) applied to a cracked member in structure. This gage measures the strain distribution around the crack tip and the measured strain is transformed into stress intensity factor. The accuracy of the measurement of the stress intensity factor is within ±10 percent compared to the exact value. Using this gage, the stress intensity factor can be measured directly under service conditions for an actual structure. It is expected to be a useful tool for the prediction of fatigue crack propagation life.

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Corrosion fatigue crack initiation behavior of low alloy steel has been investigated in water. It was observed that corrosion fatigue process was composed of three stages, namely, corrosion pit growth, transition into crack from the corrosion pit and corrosion fatigue crack propagation. The corrosion pit size was found to increase with time t following the relation : corrosion pit size ∝ t^1/3. The condition of transition into crack from the corrosion pit was determined by a stress intensity factor, by assuming the corrosion pit as a sharp crack. The critical pit condition (ΔK)_p was 1.2 MPa √(m) for 2.5 NiCrMoV and 3.5 NiCrMoV in 90°C water with 100 ppb dissolved oxygen. Based on the abovementioned results, residual life prediction method for corrosion fatigue crack initiation was proposed.

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Rotating bending fatigue tests were carried out on plain specimens of a low carbon steel at an elevated temperature. The main results obtained are as follows : (1) The Weibull distribution is well fitted to the distribution of crack length. (2) The dependence of the shape parameter of the Weibull distribution on the test temperature is hardly recognized. (3) The crack growth rate is proportional to the crack length in the main part of the crack propagation process at the elevated temperature, the same as at room temperature.

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Fatigue crack growth tests were carried out on P/M (Powder Metallurgy) aluminum alloys, 7090-T7, Al-12Si-5Fe, Al-15Zn and Al-2C, in air under ΔK-increasing and-decreasing conditions. Crack growth rates and crack closure behavior were investigated in detail by using the unloading elastic compliance method. The crack opening ratio U was found to depend on the roughness of the fracture surface. The fracture ductility of material ε_f was found to exert a considerable effect on the fatigue crack growth rate of the intermediate region, and the following empirical equation was proposed to account for the effect of material properties on the crack growth rate ; da/dn = 4.87×10³(ΔK_eff)/(Eε^0.2_f))^2.7 The fracture toughness of the materials was hoped to be increased to obtain the improved fatigue crack growth resistance in the high growth rate regime.

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In order to clarify the fatigue behavior in plain specimens of a flake graphite cast iron (FC 25) and a speroidal graphite cast iron (FCD 45), torsional fatigue tests and optical microscopic observations were made successively, on the fatigue processes by using the plastic replica method. The process was then compared to that under rotating bending fatigue. The main results obtained are as follows. (1) The fatigue limit, in each case, is determined by the limiting condition for propagation of the microcrack initiated from graphite. (2) The ratios of the fatigue limit in reversed torsion to that in rotated bending were about 0.9 and 0.8 in FCD 45 and FC 25, respectively.

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The volume fraction of strain-induced α' martensite was measured by X-ray diffraction analysis on the fracture surfaces caused by fatigue impact and standard fatigue. The volume fraction of α' martensite increased with increasing ΔK regardless of fatigue impact and standard fatigue. In standard fatigue, this volume fraction increased with increasing stress of ratio and depended on the effective stress intensity range, ΔK_eff, at crack tip. If the relation between the volume fraction of α' martensite and ΔK_eff in standard fatigue could be used to estimate the effective stress intensity factor, we can get the ΔK_eff in fatigue impact. Thus the ΔK_eff in fatigue impact was almost equal to maximum stress intensity, K_max. The fatigue crack growth rate related to the volume fraction of α' martensite, in spite of fatigue impact, standard fatigue and stress ratio. Hence, the plastic zone formed under fatigue impact should be smaller than that from standard fatigue.

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The local strain approach is a very useful method to evaluate fatigue strength of complicated welded structures. In the local strain approach, the accuracy of measured local strain is very cirtical. The effects of the radius of toe grinding and the strain gage length on the accuracy of measured local strain and Δσ(= E·Δε) - N_c curves were examined in this study. An accuracy of 90% could be obtained for the measured local strain when the length of the strain gage was less than half the toe radius. For the measured local strain, a Δσ(= E·Δε) - N_c curves for welded structures agreed with that of the small round specimen. However toe grinding caused a decrease in the local strain, and as a result, Δσ decreased with a derease in strain concentration factor. The Δσ(= E·Δε) - N_c curves modified with toe grinding radius were proposed, and the results agreed with the test data for welded structures.

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In order to understand the overall shape of the yield surfaces (rigorously defined as the loading surfaces or offset yield surfaces) of prestrained metals, the shapes of various intersections of several planes and cones with yield surfaces are investigated. The yield strength at each intersection is evaluated along the angle which is measured from the prestrained direction in the stress space. Though the data obtained from the experimental results were unrelated, the trends of yield strength are similar with each other. The similarity is especially excellent in the case of the uniaxially prestrained mild steel. This fact suggests that the yield surfaces of prestrained metals have the shape of the rotational symmetry, with the rotational axis in the prestrained direction.

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As an example of transient thermal stress problems expressed in rectangular curvilinear coordinates for which no analytical solutions have been reported, analytical solutions are presented for a transient two-dimensional temperature field and an associated thermal stress problem in an elliptical plate expressed in elliptical co-ordinates. The transient temperature function of the elliptical plate subjected to an abrupt change in temperature on the elliptic boundary can be expressed in the form of an infinite series, including Mathieu and modified Mathieu functions of the first kind of even integral order. The associated thermal stress problem can be formulated in terms of thermoelastic displacement potential and Papkovich-Neuber's stress functions. Numerical calculations are carried out for the distributions of circumferential thermal stress on the elliptic boundary and the major and minor axes in the elliptical plate for three cases of eccentricity.

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The present paper is concerned with transient thermal stresses in a transversely isotropic infinite circular cylinder inserted into a short rigid heated circular ring. This subject is a mixed boundary value problem, and may be formulated in terms of a dual-integral equation which is reduced to a simultaneous algebraic equation applying the Neumann series. The radial, hoop and axial stresses have singularities at the end of the contacted short circular ring on the cylindrical surface. The factors are defined to evaluate the singularities of the stresses, and the relations among these factors can be derived. Numerical calculations of thermal stresses were carried out for a graphite which possesses transverse isotropy, and compared with those derived under isotropic conditions.

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Many thermoelastic problems concerning point heat sources in the plane have already been treated by investigators, but the problems concerning the line heat sources have not yet been completely solved. In this paper, the thermal stresses are analyzed in the case that one line heat source exists on the infinite plate with a circular hole having a boundary of zero temperature, and that all the heat flowing out from the line heat source flows out from a circular hole under the steady-state feat conditions.

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The thermoelastoplastic stresses caused within a low-alloy steel rotor shaft material in water cooling are dynamically simulated by applying the finite element method and the incremental strain theory. The thermal stress concentration at the fillet of the model with thermal constants and mechanical properties varied due to temperature is explained according to contour lines of stress. Then, it is considered that there are sufficient capabilities for the fracture in applied positions, though the equivalent stresses exceed the yield point under the proper temperature at both surfaces of the fillet and longitudinal center of shaft. As the result, the variable principal stress ratios at the fillet are obtained through comparison with the tangential stress at the surface in the middle of the shaft, which rapidly increases in the beginning of cooling.

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In order to investigated the change of impact resistance by notch radius of steel protected from tufftriding by an inorganic coating, Charpy impact tests are carried out at various temperatures, using protectively coated specimens with notch radii of 1 R and 2 R for various treatment times. The impact transition curves, the transition temperatures and the fracture behavior are discussed by comparing them with both tufftrided and non-tufftrided steels.

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Structures of machine parts subjected impact load often suffer unexpected damage, which is remarkably different from the observed in static cases. Generally, the reflection and interferference of stress-wave play an important role in dynamic cases, and it is desirable to study the time variation of the stress distribution, and especially the value of dynamic stress concentration factors around the boundaries of different kinds of materials. Hence, we analyzed stress propagation and dynamic stress concentration phenomena around the boundary of different kinds of materials in a plate by utilizing the strain gage method, the dynamic photoelastic method and also the finite element method. We found that two-dimensional dynamic stress concentration factors obtained by the present three methods are in general agreement and if the ratio of E₂ (young's modulus for the different materials)/E₁ (young's modulus for the matrix) is small, the dynamic stress concentration factor is small, but the position of maximum stress occurs at the circular bounday of the matrix. On the other hand, if the ratio of E₂/E₁ is large, the dynamic stress concentration factor is large, and the position of maximum stress occurs at the boundary of the circular hole in various types of materials.

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In order to obtain a dynamic stress expression in a finite body subjected to an impact load, a theoretical study and experimental studies using PMMA rod specimens are carried out. An impact load induces a complicated dynamic stress sate in a finite rod. Such a stress pulse height depends on the specimen length and the supporting condition at both ends. In come materials, the stress attenuation during the wave propagation will also affect the pulse height. Including these influences, the expressions of dynamic stress are derived for an impact compression and for a torsion. The coefficient of reflection at the ends of a bar and the attenuation coefficient are evaluated in terms of the strain gage method. Theoretical results given in the available form shoed fairly good agreement with the experimental results.

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A simple procedure for the determination of stress intensity factor K for the problems whose solutions cannot be obtained easily by numerical analysis is proposed. The method is based on the concept that if we choose two referential two-dimensional problems and two geometrically similar three-dimensional problems, the ratio of K in the three-dimensional problem is approximately equal to that in the two-dimensional problem. The accuracy of the solutions depends on the choice of referential problems. The applicability of this method is checked by applying it to a semi-elliptical surface crack in a finite-thickness plate and an edge crack in a plate with finite width. Finally, the stress intensity factors for a semi-elliptical surface crack in a round bar under bending are obtained by the proposed method, in which a plate with an edge crack under tension and bending and a shaft containing a semi-elliptical surface crack are chosen as referential problems.

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This study is concerned with an application of the Boundary Element Method (BEM) to 3-dimensional thermal elastic plastic analysis. A new procedure of thermal elastic plastic analysis is proposed to consider the temperature dependence of stress-strain curves and to introduce multi-linearized stress-strain curves into boundary element analysis. Some numerical techniques for BEM such as traction discontinuity treatment and tying condition were also introduced into analysis. The accuracy of 3-dimensional thermal elastic plastic analysis was confirmed by performing a thermal elastic plastic analysis of a thick-walled cylinder.

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The Moire fringe technique is presented as a method of measuring inhomogeneous distribution of small strain. The method was applied to the measurement of the plastic strain profile near the running Luders band front in twisted thin wall bars of mild steel. A fine Moire grid pattern was photo-printed on the curved surface of the bar. The material constants of the yield initiation condition in shear were obtained from the measured strain profiles.

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The temperature dependence of the multiaxial cyclic behaviour of type 316 stainless steel was elucidated experimentally. Cyclic tests under constant total-strain amplitudes were performed for uniaxial tension-compression and circular strain paths at several temperatures ; room temperature, 200°C, 400°C, 500°C, 600°C and 700°C. The strain amplitudes of the cycles were specified to be 0.2, 0.3 and 0.4% under constant strain rate of 0.2% /min. It was observed that though strain hardening for circular cycles was larger than that of the tension-compression cycles at every temperature, the effect of nonproportionality in cyclic hardening decreased with the increase in temperature. The cyclic hardening was significant particularly in the temperature range between 400°C and 500°C.

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Uniaxial and equibiaxial strengths of soda-lime glass specimens having a controlled surface flaw introduced by Vickers microhardness indentation were determined in both four-point bend and concentric-ring loaded-disk tests. The tests were conducted at three or five stressing rates in both air and pure water environments. Tensile strength increased with the stress rate for each loading condition, and the data could be represented by a straight line on a logarithmic plot of fracture stress as a function of the stress rate. The tensile strength and the gradient of the increase in the strength were greater for the biaxial tension mode of stressing than for the uniaxial mode in the water environment, though there was no significant difference between biaxial and uniaxial stressing in air. The stress state effect in a water environment could be explained by assuming that the rounding of the initial crack tip was caused by the reaction of water with the glass at the crack tip.

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Several criteria are proposed to predict the failure bending moment of a pipe which has a circumferential crack and is subjected to external bending moment in LWR (Light Water Reactor) pressure boundary piping. However, those criteria give an unconservative prediction when the pipe has a short and deep circumferential surface crack. This paper presents a half-empirical criterion on the basis of the test results. This criterion gives a conservative prediction by choosing the optimum parameter, even if the pipe has an arbitrary circumferential surface crack. This paper also presents a method to calculate a tearing modulus, T_appL, of the pipe containing the circumferential surface crack just after the ligament failure. Moreover, the compliance of a four-point bending machine is converted to an equivalent pipe length, which is used to calculate the value of T_appL.

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The authors are performing an unstable fracture test of circumferentially cracked pipes in order to investigate the possibility of mitigating the conservative assumption of guillotine break in light-water reactor pressure boundary piping. The tests were performed at 285°C and at 6.86 MPa using type 304 stainless steel pipes of 165.2 mm in diameter and 11.0 mm in thickness. It is concluded that the predicted fracture load by the net-section-stress approach is conservative in a limited range of crack dimensions.

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The initiation condition of creep crack growth was studied by using the crack energy density ε as the creep crack parameter. That is, the creep tests of CT specimens of Al alloy were carried out by varying the level of load and the corresponding values of crack energy densities were evaluated by finite element analyses based on the ε_j-integral, which is path independent without any restriction on constitutive equations. The characteristics of crack energy densities at the initiation times of creep crack growth were discussed, and the initiation condition, in terms of crack energy density, was considered. The results are as follows : (1) The critical value expressed by total crack energy density ε( = ε_0⁺ +ε^(cr) +ε_0⁺ : elasto-plastic contribution at the time of load setting, ε^(cr) : additional part caused by creep deformation) depends on the level of ε_0⁺. On the other hand, (2) the critical value expressed by ε^(cr) seems to be nearly independent of the level of ε_0⁺. Therefore, (3) ε^(cr) may be used as a useful parameter for the evaluation of the initiation condition of creep crack growth.

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The behavior of ductile crack initiation from a notch and a crack under mode I loading has been investigated on structural steel SM 41 A. Experiments and large deformation finite element analyses based on Gurson's yield function were carried out for three-point-bending specimens with a notch are a crack. In the notch-specimens, void growth behavior around a notch tip is described by the void volume fraction obtained by the finite element analysis, and the ductile crack initiation can be predicted based on the concept of the critical void volume fraction. In the finite element analysis of the crack-specimen, the large strain field-process zone-around a crack tip is characterized by the void volume fraction. From the comparison of experimental results with analytical results, it is suggested that, in order to predict the ductile crack initiation from a crack based on the concept of the critical void volume fraction, the correlation between the size of a large strain field and the spatial distribution of inclusions should be taken into consideration.

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In the previous paper, it was shown that the strain energy release rate at brittle fracture initiation could be employed as the criterion for the ductile-to-brittle transition in the Charpy test. In this paper, the relation between the strain energy release rate at the temperature of the ductile-to-brittle transition region and the fracture toughness at low temperature is discussed. For the purpose the Charpy impact test for specimens with pre-fatigue crack and the three point bending fracture toughness test were carried out. Consequently, it was shown that the strain energy release rate corresponded to the fracture toughness obtained from the three point bending test in accordance with the ASTM E 399-72 standard.

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The evaluation procedure of cleavage mode fracture toughness is discussed on the basis of combined elastic-plastic fracture methodology, AE (Acoustic Emission) technique and statistics, where the AE method determined the onset of microscopic cleavage pop-in cracking. The intergranular cleavage fracture toughness data obtained for temper-embrittled Cr-Mo-V steel at 150°C were mainly analysed for the probabilistic aspect, and their size effects were also discussed. The main results are : (1) Population of the intergranular cleavage pop-in fracture toughness could be represented by a three parameter Weibull distribution function. (2) Distribution of the intergranular cleavage fracture toughness on large specimens can be predicted by the fracture toughness data using small specimens which satisfy a size requirement, B>150·(J_c/σ_Y), and this is also applicable to the evaluation of transgranular cleavage fracture toughness. (3) A probabilistic procedure for predicting a lower bound cleavage mode fracture toughness is proposed based on the above results.

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The dynamic fracture surface formation of PMMA and epoxy was studied. Fracture parameters such as crack velocity a^^· and crack extension resistance R^* were obtained by high-speed photography of fracture caustic images. The density of surface marking was also obtained by examination of the fracture surfaces. Correlations between the density μ and the fracture parameters have shown that, although μ depends on a^^· or on R^*, μ is not a unique function of one of those parameters. It is found that μ has the best correlation with the product R^*· a^^·, i.e., dissipated energy per unit crack front and unit time.

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A design guide is proposed to assure the safety and the reliability of fine ceramic components which operate under mechanical and thermal loads. The guide is intended to keep the fracture probability of components below a certain allowable level in the fast fracture. This is attained by satisfying a design formula written in the guide which limits the maximum stresses of some specific sections of the compoent to an allowable value. The allowable stress value is given by the combination of the material strength, three design factors and two safety factors. It should be noted that the proposed design guide is given only tentatively, and should be refined and extended through experiences.

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Silicon carbide plate specimens with through-thickness crack of which stress intensity can be calculated by the two-dimensional stress analysis, are prepared by a new method developed in the present work for conducting fracture toughness tests. The specimen geometry is quite similar to that of ASTM standard compact tension specimens. A compressive load is applied on the upper and lower surfaces of the specimen, with a narrow slit crack-starter to produce a tensile stress near the notch root and a compressive stress far from it. The loading points is changed by the required crack length. Then, the specimen is loaded by a 20μs bending moment at the notch root. The obtained fracture toughness value from the specimen is almost constant, in the range of the crack length between 0.4 and 0.7 in its ratio to the specimen width. It is also independent of the specimen thickness between 3.0 and 9.5 mm.

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This paper deals with the strength characteristics of combination joints of adhesions with bolts. Firstly, the stress distributions in adhesives and the variant of bolt axial force are analyzed when an external load is applied to the combination joint, in which two hollow cylinders are clamped by a bolt and a nut with an initial clamping force after they are joined by an adhesion. For verification, experiments are performed. Analytical results are in fairly good agreements with experimental ones. Then, it is seen that the strength of the combination joint is greater than that of the adhesive joint and that the variant of bolt axial force in the combination joint is less than that in the bolted joint. In addition, the strength characteristics of T-type butt adhesive joint combined with bolts from both analyses and experiments are discussed. The characteristics of combination joints are made clear.

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Bonding strength of a metal (Fe-Ni alloy) and resin (epoxy base) adhering interface was examined under thermal stress which was caused in the cooling process of the thermoset resin after adhesion. The thermal stresses on the adhering interface were calculated using the Finite Element Method. These calculated stresses and the experimental strength were compared. The following results were obtained. The bonding strength of a metal and resin adhering interface under thermal loads can be estimated mainly by using shearing stress on the adhering interface (τ_yz). Further accurate strength estimation can be obtained by taking into account the normal stress on the adhering interface (σ_z).

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The strength evaluation of pin joints for crane structure, which are subjected to tensile loads, by experiment and by stress analysis using FEM is presented. The yield as the joint occurs at about 2.3 times the tensile load, where the maximum tensile stress of the pin joint reaches the yield point of the material. The yield strength can be obtained, for practical usage, either as the tensile stress of the net area transversing the load axis or as the shear stress of the tear-out section area in the direction of the load. The former stress depends on the ratio R/γ (R : the outer radius of the joint, γ : the pin radius), the latter stress is independent of the ratio. FEM analysis shows that the general yield of the joint occurs when the yield area expanding from the inner edge of the pin hole combines with the other yield area expanding from the top of the joint. The fracture mode of the joint depends on the ratio R/γ.

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The small and light weight motor generator with permanent magnets is available in the field of a high-rotational-speed machine. The authors have developed a new-type uninterruptible power system with a high speed flywheel. This system carries continuous power to a computer immediately from the flywheel storage unit by changing kinetic energy into electric energy if the primary power source is temporarily interrupted. In this system, a cylindrical-type, synchronous motor generator with permanent 2-pole magnets on the inside periphery is adopted. The flywheel rotor rotates continuously at a high rotational speed of about 30 000 rpm. The stress and strain in the flywheel rotor is caused by centrifugal force. This stress and strain occurs in the rotor magnet at the same time. A crack in the permanent magnet would occur if the flywheel rotor were to reach a higher rotational speed because the material of the permanent magnet is brittle. This paper presents a mechanical strength evaluation of the permanent magnet in a rotating machine.

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An analytical method for the elasto/visco-plastic problems of general, orthotropic moderately thick shells of revolution subjected to asymmetrical loads is developed in consideration of the effect of shear deformations. The Reissner-Naghdi theory for elastic moderately thick shells is extended in this analysis. As the constitutive equation, Hooke's law for orthotropic materials is used in the elastic region, and equations based on the orthotropic visco-plastic theory derived from the orthotropic plastic theory by Hill are employed in the plastic range. The visco-plastic strain rates are related to the stresses by Perzyna's equation. In order to check the adequacy of the numerical analysis, experiments are performed on the elasto/visco-plastic deformation of a titanium cylindrical shell subjected to locally distributed loads. Good agreement is obtained between the experimental results and analytical solutions. The fundamental equations for the increment are numerically solved by a finite difference method and the solutions are obtained by integration of the incremental values.

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This paper presents an efficient calculation method which eliminates the LDU decomposition process of the stiffness matrix in numerical solution s of the finite element method (FEM). As an example, this method is applied to an elastic analysis of variable cross sectional beams with shear deformation. The FEM using this method decreases CPU time and memory capacity in comparison with conventional FEM using the LDU process. Moreover the use of the method makes the FEM algorithm simple, and gives more accurate results. Therefore, this method is effective for microcomputer aided FEM.

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The stiffness matrix of a 4-nodes isoparametric element for the two dimensional finite element analysis is evaluated using the symbolic mathematics system, called REDUCE. The results are compared with those obtained by numerical integration. It is shown that these exist some differences between the numerical values of the stiffness matrix by symbolic and numerical integration. The differences become smaller due to the increase of the integration points in the numerical integration, which means that the results obtained by symbolic integration give accurate values. The stiffness matrix in elastic-plastic state is also evaluated using symbolic mathematics, and it is shown that the numerical results agree with those obtained by numerical integration. It is pointed out that it is possible to decease the CPU time by using the symbolic mathematics system.

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Recently by putting supercomputers to practical use, there is the possibility of solving large scale structural problems using the finite element method with high computing speed. The authors have developed a high-speed structural analysis program, named SIMUS, applying algorithms suitable for the supercomputer HITAC S-810. This program showed ability to solve very large scale problems, for example, 10 077 nodes in short computing time.

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This study aims at investigating the performance of a hardness testing machine. First, the phenomenon of a contact between a rigid sperical indenter and a plastic material is considered. By using Hertz's elastic contact law, the Young's modulus of plastics Es can be calculated from Eq. (1) using the cordal diameter of an indentation d, the elastic recovery of an indentation δ_r and the indenting load L : E_s = 0.9(3/2) L/(d δ_r)…(1) From the geometrical relation at the contact part, the contacting diameter d_c and the surface level diameter d_l are derived as follows. (δ_t : the total depth) : d_c = 2[D(δ_t-δ_r/2){1-(δ_t-δ_r/2)/D}]^1/2…(2), d_l = 2[Dδ_t×(1-δ_t/D)}^1/2…(3) Furthermore, the mean strain rate under the elastic recovery by a spherical indenter is related to the strain rate under the uniaxial stress field. Finally, the indenting experiments are carried out, δ_r and δ_t are measured so that a cordal diameter d is formulated as follows : d = d_l{1.71-0.707(d_l/d_c)}…(4) When the Young's moduli calculated from δ_t and δ_r using Eqs. (1)-(4) are compared to the Young's moduli measured from a compression test, their Young's values consist within an accuracy of about ±5-10%. Therefore, the measuring method about Young's modulus of plastics using the indenting hardness test by a spherical indenter can be applied to the present hardness testing machines.

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