New method to determine the mechanical properties of heat treated steels

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Abstract

A new numerical approach to indentation problems is developed for hardened materials. A relationship between load, displacement, flow stress and strain hardening exponent of heat treated materials with a hard film, is given.

This method is based on the minimisation of the error between the experimental curve (load–displacement of the indenter) and the theoretical curve, function of the mechanical and geometrical properties of the studied materials.

Comparison of the numerical results with those experimentally obtained from known materials confirms the interest of the method proposed.

Introduction

Surface heat treatments concern many parts of machines particularly exposed to corrosion, friction and high pressure. Different techniques are available to carry out superficial heat treatment (carburiding, nitriding, carbo-nitriding, induction hardening, etc.). The main ultrasonic waves techniques, or the eddy current method, are difficult to set up. Moreover, they are highly sensitive to parameters other than hardness. Therefore, in spite of many disadvantages such as the destructive aspect, or increased costs caused by the slowness of the procedure, the Vickers micro indentation technique is still commonly used in industry.

There is a real need for a method to characterise the mechanical properties of such materials having undergone thermal hardening; the problem is especially difficult for hard, thin ones. Hardness tests are excellent candidates for this purpose. However, hard films tend to transmit the deformation to the softer substrate, and the measurement is a compromise between the hard surface and the substrate properties. A possible solution is to use lower loads, in order to limit deformation to the hardened layer (nanoindentation technique) by respecting the ‘1/10th rule’ [1], which states that the substrate does not perturb the measurement of the hardness if the indentation depth is smaller than 0.1 times the hardened thickness. An alternative consists of constructing precise models of the influence of the substrate to obtain the intrinsic mechanical properties of the layer from usual micro-indentation techniques.

For materials with a hard film, analysis of the strains and the stresses is then used to explain or predict the failure of the hard film. This can lead to optimising the layer in terms of its thickness or material properties.

Modelling the deformation of heterogeneous materials is never an easy task. Some results could be obtained for elastic or perfectly rigid bilayers by rather simple techniques giving closed-form solutions. However, the strongly elastoplastic character of most heat treatments made it necessary to use more general methods, namely finite element techniques, now widely used for the analysis of strains and stresses in materials having sudden thermal processing. The negative counterpart is that parametric studies become excessively long and tedious.

Indentation experiments have been performed for nearly 100 years for measuring the hardness of materials. Recent years have seen increasing interest in indentation because of the significant improvement in the indentation equipment and the need for measuring the mechanical properties of materials on small scales. From the load–displacement curve of an indenter during indentation, the hardness and Young's modulus (for example) may be obtained from the peak load and the initial slope of the unloading curves.

The indentation measurement consists of pushing an indenter into the sample under precise load control. The initial rate of change following the decrease in force (i.e. the slope) is defined as the sample stiffness. In a standard nanoindentation measurement, the indenter is inserted into some specified depth and then extracted, giving the loading force over the whole depth range. One has a value for stiffness only at the deepest portion of the test. For a bulk sample or a relatively thick film, analytical methods have been developed to deduce hardness H and Young's modulus E from the data [2], but H and E are deduced only at the deepest penetration. For a thin layer, such an analysis yields values for H and E that are due to the combined response of the layer and the substrate.

As early as the 19th century, one sees the work of Hertz on rubbers appearing. Indentation of rubber can be interpreted in terms of elastic parameters using Hertz's theory [3] for a spherical indenter, or using Sneddon's equations for conical indenters [4].

For metals in plastic state, Tabor [5] was the first to point out the relation between the Vickers or Brinell hardness and yield stress σy, namelyHV≈3σyandHB≈2.8σy.This experimental observation was backed up by theoretical analyses of plastic flow, based on the Slip Line Fields method for spherical indenters [6], for a cone [7] and the generalisation to the Vickers pyramid by Haddow et al. [8]. These studies confirmed the value of H≈3σy for blunt indenters, and also derived solutions for sharper indenters.

Purely plastic analyses proved insufficient for hard metals, where elasticity cannot be neglected. Following the observations by Marsh [9], an analogy with the classical problem of the growth of a cavity in an infinite elastoplastic medium was used to determine the relationship between the hardness number (or average indentation pressure) and parameters mixing geometry with elastic and plastic properties of the indented material [10], [11].

Mechanical analysis requires formulation of the sharp indentation problem which is inevitably three-dimensional and at first glance seems quite impossible to solve, mainly because of material and geometric nonlinearities, various dissipative mechanisms such as plasticity, phase transformation, microcracking and the presence of residual stresses [12]. The properties of the indenter, such as its sharpness, are also very important for the analysis. The combination of all these effects makes the problem difficult to address analytically, and for this reason it was left unsolved in the past. Today's computational capacity is, however, sufficient for a detailed investigation of the important features of sharp indentation tests. Considerable theoretical and numerical experience was drawn from especially the work on the Brinell test (spherical indenter) by Hill et al. [13] and Storakers and Larsson [14] and also on the Vickers test by Giannakopoulos and Larsson [15] and Giannakopoulos et al. [16]. For the problems for which the indenter has an axisymmetric form (cones and spheres, etc.), a model using two-dimensional finite elements (2D) often remains sufficient.

The aim of this work is to find the mechanical properties of thermally treated steels with a thin film and a rather high hardness gradient, still based on instrumented indentation techniques and numerical methods.

The hardened steel is assumed to be elastoplastic. This chilled steel comprises a film with a very hard low thickness compared to that of the substrate. It will thus be regarded as a bilayer. The indenter keeps its shape and is perfectly elastic and axisymmetric.

An evolution law yielding the indenter displacement versus the mechanical properties of materials is obtained and validated experimentally.

Section snippets

Hardness-flow stress relation

The spherical cavity expansion model expresses the hardness to elastic modulus ratio (H/E) as a function of the flow stress to elastic modulus ratio (σy/E) for materials that are very hard or elastic. Thus, the linear hardness-flow stress correlation obtained from the Slip Line Field theory can be rewritten in terms of H/E and σy/E. Due to the 1/E dependence in these relations, the elastic modulus was used as the normalising parameter. As the first step in developing the hardness-flow stress

Spherical indenters

The relationship between load F and the characteristic contact displacement δ represents an important material characteristic in indentations with spheres of radius R. Spherical indenters are widely studied experimentally, because of their relative simple geometry, and theoretically, because of their facility to provide essential information on both elastic and plastic deformation properties of the test material. By defining indentation stress, F0=F/πa2 (a is the contact radius) (Fig. 1) and

Experimental procedure and material

A brief description of the experimental procedures is given in this section. The schematic set-up of the test apparatus is shown in Fig. 3. This indentation device is used to measure the F-δ values during indentation. It was obtained with a load cell, displacement gauge and a spherical indenter (with a standardised sphere diameter D=1.587mm).

Indentation depth δ was monitored using a displacement gauge mounted on the base, which sensed the displacement of a steel arm mounted in very stiff load

Procedure for a homogeneous material

The aim of this paragraph is to determine the flow-stress and strain hardening exponent starting from an instrumented test of indentation.

Initially, we will be interested in the case of an isotropic and homogeneous material. Thereafter, the various results obtained for homogeneous materials will be extended to the case of non-homogenous materials.

For a homogeneous material, we seek to express the displacement δ of the indenter according to load F. The selected function will be written as

Procedure for non-homogeneous materials

Steels have undergone a surface heat treatment and present a hardened fine layer (film) which varies from a few hundredths of a mm to several mm. For film thickness exceeding one tenth of a mm, drilling techniques were developed to approach the hardness of the treated steels [21]. The case which interests us and for which traditional techniques do not give satisfactory results, is the case of very small thickness.

One can consider that these materials consist of two almost homogeneous layers (

Identification procedure of the mechanical parameters for a bilayer

The studied sample (Z38CDV5 steel) is cylindrical, with a diameter of 1.5cm and length of 1cm (Fig. 16). The mechanical characteristics of the substrate areν=0.3,E=210GPa,σys=480MPa,ns=0.25.

This sample has undergone a nitriding treatment, which caused a hardening of a fine layer with thickness ef equal to 0.11mm (Fig. 16). Microindentation Vickers tests on the substrate and on the fine layer lead to have the values of 420HV for the substrate and 670HV for the fine layer (Fig. 5). Fig. 16 gives

Conclusions

The mechanical behaviour of a bilayer depends on the geometric and mechanical properties of both of its components. Formula (19) is a law of the mixtures which takes into account the influence of film and substrate. This influence is modelled by parameter α. Certain expressions of α have been proposed in the literature [23]. These expressions were improved in order to take into account film and substrate plastic energies under indentation deformation. Model (25), which considers the plastic

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