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The impact of various cooling environments on the distribution of macroscopic residual stresses in near-surface layers of ground steels
Materials Science and Engineering A 497 (2008) 200–205
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Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
The impact of various cooling environments on the distribution of macroscopic residual stresses in near-surface layers of ground steels Z. Pala ∗ , N. Ganev Department of Solid State Engineering, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Prague 2, Czech Republic
a r t i c l e
i n f o
Article history: Received 5 December 2007 Received in revised form 30 June 2008 Accepted 2 July 2008 Keywords: X-ray diffraction analysis Residual stress distribution Shear stresses Grinding Cooling Electro-chemical polishing
a b s t r a c t Grinding often plays the role of final machining, and, therefore, its parameters significantly affect the properties of the treated surface. In this study, the state of surface residual stresses (RSs) and their depth distribution into the bulk is investigated with respect to various cooling environments during grinding. In order to acquire complete stress tensors, the sample surfaces were analysed using the X-ray diffraction technique. Since ε (sin2 ) dependences in grinding direction are non-linear and exhibit psi-splitting, the method proposed by Dölle and Hauk was used to evaluate the tensors of anisotropic triaxial state of RS. The effective penetration depth of Cr K␣ X-ray radiation into ferrous materials is approximately 4 m, and, therefore, removal of surface layers is necessary in order to pinpoint the distribution of RSs beneath the surface. The process of electro-chemical polishing ensures that the impact of material removal causes minimal or negligible mechanical and thermal distortions of the investigated state of stress. © 2008 Elsevier B.V. All rights reserved.
1. Introduction The grinding process can be employed at several stages of the manufacturing of machine components. The difference rests both in the modes and parameters of grinding. The depth of cut (thickness of removed layer) and wheel speed play a large role in determining whether the grinding is smooth enough in order to be the last step in the whole chain of manufacturing procedures. The goal of finish grinding is, above all, to achieve a high quality surface according to the requests of the customer. The appropriate choice of grinding parameters, material of grinding wheel abrasives and form of cooling has a relevant impact on the final quality. In order to obtain the proper conditions, it is necessary to take measurements of structural parameters of the surface. It is widely accepted that the state of residual stress (RS) on the surface and the near-surface area belongs among the most important parameters of surface quality. Macroscopic RSs may significantly affect the fatigue limit and wear life, and it could even increase the corrosion resistance. It has been shown [1] that, in general, compressive residual stresses in the material can favourably reinforce the dynamic strength by about 50%; on the other hand,
∗ Corresponding author. Tel.: +420 224 358 624; fax: +420 224 358 601. E-mail address: zdenek.pala@fjfi.cvut.cz (Z. Pala). 0921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2008.07.001
tensile RSs could reduce the dynamic strength by about 30%. Such advantageous effect of compressive RSs can be derived from mechanical model of counterbalancing, when the RSs mitigate the adverse effects of tensile load stresses [2] that occur during the service. Various techniques exist to determine RSs in materials; yet, out of the non-destructive methods, X-ray diffraction plays a prominent role because of its availability and accuracy. In combination with layer removal by electro-chemical polishing, stress gradients from the surface can be established and studied. The use of electrochemical polishing [3] can only be avoided if synchrotron radiation, which enables the variation of wavelength and hence adjustable penetration into material, is available. The conception of RS distribution in near-surface layers of a ground sample is based on the assumption of the inhomogeneous plastic deformation due to (i) mechanical interaction between the wheel and ground surface; (ii) equalization of temperature between the grinding zone and its environment [4]. In case of high grinding temperature (iii) phase transformation may occur, this would lead to an origination of transformational RS due to changes in crystal lattice [5]. The result of mechanical surface treatments with a tangential component, like milling, turning or grinding is inhomogeneous plastic deformation in the near-surface area resulting in RS due to the greater relaxation of this region compared to the bulk [6]. Plastic deformation of the surface layer inherently changes its
Z. Pala, N. Ganev / Materials Science and Engineering A 497 (2008) 200–205
Fig. 1. Dependences of 2 2 1 1 (sin2
201
) for low carbon 16MnCr5 steel ground with a liquid coolant.
volume which is reflected by a creation of elastic deformation in the adjacent zone [7], moreover, the plastically deformed layer acts as a barrier to full relaxation of elastically deformed areas of the material. This process of mechanical deformation (Herzian pressure) leads to compressive stresses on the surface, whose magnitude diminishes with increasing depth. Thermal RSs are created due to initial expansion of material in the grinding zone which is swiftly followed by a contraction owing to temperature levelling off between the grinding zone and its neighbourhood. It can be supposed that the ground surface itself embodies the point from which heat is conducted into the material. The amount of this heat ε, which is usually defined as a percentage share of the total heat output, is affected by a range of factors, among them the most decisive being the material of abrasives, the cooling of the surface, the grinding parameters, etc. The value of ε for conventional grinding conditions without cooling, for the corundum grinding wheel and common steels was established between 60 and 75% [8]. The quasi-steady temperature profile throughout the whole sample can be analytically computed according to the model of triangular heat source proposed by Jaeger [9] and Carslaw and Jaeger [10] if the ε is known. While the whole system strives to get into equilibrium the temperature profile dramatically changes over the course of time. The temperature on the very surface decreases rapidly, forming a barrier for cooling the near surface and bulk areas which are yielding to thermal expansion. Tensile RSs prevail on the surface only if thermal stresses surpass the yield stress of the material [4,5]; otherwise compressive stresses are present in the surface layer, balanced by tensile stresses in the bulk. Since the yield stress is strongly temperaturedependent, i.e., diminishes with rising temperature, tensile stresses might arise even at relatively moderate temperatures. The final shape of RS distribution is superposition of mechanical, thermal, and transitional residual stresses, all of which result from inhomogeneous processes. The aim of this study is a comparison of three manners of cooling during grinding from the point of view of macroscopic RS. X-ray diffraction measurements were performed to obtain stress tensors for surfaces and for the near-surface area of the ground samples.
The steel 16MnCr5 (DIN 17210) is suitable for case carburizing; it is often used in the automotive industry for parts with a required core tensile strength of 800–1000 N/mm2 and good wear resistance, like shafts, bolts and geared wheels [11,12]. The stainless martensitic chromium steel M300 (X36CrMo17) is corrosion-resistant with a chromium content of about 16%. It is used in moulds for chemically aggressive plastics and plastic abrasive fillers; it has outstanding corrosion and wear resistance [13] and a tensile strength of 800–950 N/mm. The square samples, 50 mm in dimensions, were 5.5-mm thick. All samples were first annealed at 550 ◦ C in an argon atmosphere for 2 h; the fall in temperature after annealing was gradual in order to rule out any additional thermal stresses. Two annealed samples, one from each material, were used for determining the unstressed lattice plane spacings. The finish surface grinding was conducted on the BPH 320 A face grinding machine. The identification label of the grinding wheel used designating its characteristics was 1 - 250 × 32 × 76 A98 60 K 9 V01–50 m s−1 ; just to highlight the significance of some symbols: the numbers 250 × 32 × 76 represent the dimensions and A stands for aluminium oxide (corundum) abrasive. The samples were fixed on a magnetic table, which was translating in respect to the grinding wheel rotation axis, and, hence, enabling the alternating processes of down-cut and up-cut grinding. The grinding conditions were as follows: the wheel speed: 35 m/s, tangential speed of table drift: 10 m/min, axial table drift: 1 mm per stroke, and thickness of removed layer: 0.02 mm. The grinding wheel was trued up after each sample in order to maintain constant grinding conditions.
2. Experimental 2.1. Samples Surface RSs and their gradients were studied in ground low carbon Mn–Cr steel 16MnCr5 and in high-carbon stainless steel M300.
Fig. 2. Effective penetration depth Te for Cr K␣ radiation into ferrous materials, -goniometer, = 80◦ .
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Fig. 3. Distribution of residual shear stress 13 in a sample from low carbon 16MnCr5 steel ground with cooled air at −28 ◦ C and dependences 2 2 1 1 (sin2 and at a depth of 50 m.
2.2. Cooling during grinding The mechanical interaction between the grinding wheel and workpiece is responsible for the increase in temperature in the area where friction takes place. A part of the emergent heat is conducted into the material and, taking into account inhomogeneous temperature fields, consequently thermal stresses arise. The creation of heat may even lead to thermal damage to the workpiece, which may severely reduce its fatigue and wear life [14]. A high level of tensile stresses may be included among thermal damages. Various cooling techniques are applied in order to conduct the heat away from the surface, and, thus, subdue tensile stress generation. Both gaseous and liquid cooling media are used. To evaluate the efficiency of cooling several parameters are measured. The distribution of RSs in the material is studied; the temperature during grinding may be measured either by thermocouple [15] or by CCD-based InfraRed imaging system [16]. Moreover, some coolants inherently also lubricate the grinding zone, which leads to a reduction of the friction between the grinding wheel and workpiece [17]. The level of lubrication can be estimated from the size of tangential and normal forces which are usually detected by piezo-electric dynamometers. In the experiment, an emulsion of water and synthetic fluid for machining operation Cimtech A31F was used as cooling liquid; the amount of incoming liquid being 5 l/min. The source of cooling air was a Ranque-Hilsch vortex tube [18]; four temperatures of air were used: 0, −10, −20 and −28 ◦ C. For comparison, one sample was ground without any cooling. 3. X-ray diffraction stress analysis The X-ray diffraction technique is a well developed and thus a widely used tool for measuring residual strains in polycrystalline materials. It is based on the assessment of lattice parameter. Changes of the lattice plane spacing dh k l are reflected by the peak position shifts in the X-ray diffraction pattern. The lattice strain εh k l is defined as a relative change of dh k l . The measured strain εh k l in the azimuth ϕ and in the tilt angle can be expressed as [19]: εhϕ k l = (ε11 cos2 ϕ + ε12 sin2ϕ + ε22 sin2 ϕ)sin2 +(ε13 cosϕ + ε23 sinϕ)sin2 .
+ ε33 cos2 (1)
If the strain is measured in six independent directions (ϕ, ), the complete symmetrical strain tensor comprising six components may be evaluated. The sin2 method stems from the proportionality of the measured strain εh k l to sin2 and is solely intended for the investigation of the biaxial stress state. There are several
) at the surface
limitations to the use of the sin2 method: (i) the texture of the investigated sample should not be pronounced, otherwise appropriate methods for evaluation of RS in textured material must be used [20], and (ii) the size of crystallites should be small (i.e., backscattering Debye–Scherrer patterns from the same irradiated volume should be homogeneous and continuous). Differentiating Bragg’s law, it can be found that the most convenient of Bragg’s angles are → 90◦ ; therefore {2 1 1} diffractions of ␣-Fe were investigated with Cr K␣ radiation (diffraction angle 2 ≈ 156◦ ) and an -diffractometer equipped with a scintillation detector. The goniometer was adjusted in reference to a strain-free reference specimen of ␣-Fe powder. The differential -method, when the azimuth is kept constant and the tilt is changing, was employed. Measurements were taken on the grinding direction (ϕ = 0◦ and 180◦ ), the transverse direction (ϕ = 90◦ and 270◦ ) and on the direction defined by azimuths ϕ = 45◦ and 225◦ ; corresponding to the positive (ϕ = 0◦ , 45◦ and 90◦ ) and negative (ϕ = 180◦ , 225◦ and 270◦ ) tilts. For each azimuth nine tilts defined by sin2 = 0; 0.1; 0.2; . . .; 0.8 were measured. The Bragg–Brentano focusing condition is fulfilled in case of -diffractometer only if the tilt is zero, and the irradiated surface, focus point of the X-ray tube and the incoming slot of the detector lie on the focusation sphere; otherwise, if the tilt is nonzero and the sample is flat, the experimental lay-out is in the so-called Bragg–Brentano parafocusing geometry. Although RSs are measured in higher 2, the deviation from Bragg–Brentano focusation when the surface is tilted (psi is nonzero) results in change of the measured diffraction profile shape. This would naturally require a misalignment correction; nevertheless, it was found out [21] that such correction would be statistically insignificant in the event of establishing the position of diffraction maximum as a centroid of diffracted doublet Cr K␣1 ␣2 . Hence this method was used after Lorentz’ polarization and temperature expansivity corrections [22]. The applied calculation of peak position does not render the misalignment correction unnecessary, but can minimize the sensitivity to deviations from perfect alignment as the integral centroid method is not as sensitive to line broadening as profile shape fitting parameters. The obtained courses 2 2 1 1 (sin2 ) exhibit psi-splitting for azimuths ϕ = 0◦ and 45◦ as shown in Fig. 1. method, Dölle and Hauk method (modified sin2 2 sin –sin (2 ) method) was implemented for calculation of the strain tensor from a+ and a− functions [23]. The calculation of stress tensor was done from the strain tensor by using the generalized Hooke’s law [24]: 1 ij = 1/2s2
εij −
s1 ıij εkk 1/2s2 + 3s1
,
(2)
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Table 1 Components of the surface stress tensor in ground samples of low carbon 19MnCr5 steel Coolant ◦
Air 20 C Liquid Air 0 ◦ C Air −10 ◦ C Air −20 ◦ C Air −28 ◦ C
11 (MPa) 105 −156 118 166 −2 −1
± ± ± ± ± ±
13 11 20 11 6 13
22 (MPa) −132 −318 −133 −101 −204 −217
± ± ± ± ± ±
16 11 14 11 7 10
33 (MPa) 61 39 70 60 70 57
± ± ± ± ± ±
8 6 9 6 3 6
where 1/2s2 = 5.76 × 10−6 MPa−1 and s1 = 1.25 × 10−6 MPa−1 are Xray elastic constants calculated according to the Eshelby–Kröner method [25] for measured ␣-Fe {2 1 1} diffraction planes. The evaluated RSs are mean values for the irradiated volume. Due to low penetration depth, the X-ray diffraction technique can be used only for surface layers of a few micrometers in thickness. The course of the effective penetration depth for diffractometer, Bragg’s angle = 80◦ and Cr K␣ radiation is shown in Fig. 2. It can be seen that the irradiated volumes vary markedly for different tilts. In order to confine information about RS to certain depth, computation of strain can be limited to tilts not larger than 45◦ or even less. For the case of conventional X-ray diffraction apparatus, investigation of stress depth profiles is carried out along with removal by electro-chemical polishing. During electro-chemical polishing the process of anodic dissolution [3] takes place. The anode is formed by the sample itself. The product of this process is a solution with high electrical resistance which is embedded into microscopic wells in the sample surface and preferential removal of roughness proceeds. However, layer removal does, by its nature, distort the original state of stress. A correction procedure proposed by Moore and Evans [26] and Sikarskie [27] exists for biaxial state of stress, which presumes that the whole surface area is being removed. This correction is often employed when shot-peened samples are investigated, but in this case of triaxial state of stress it would not be correct. An alternative attitude to this issue can exploit the finite element method: such computation [28] of stress redistribution due to the electro-chemical removal of layers has proved that distortions can be neglected if the removed area is in the centre of the sample and the removed volume is negligible with respect to the sample volume. For surface layer removal the LectroPol-5 by Struers, an apparatus for automatic, micro-processor controlled electrolytic polishing and etching of metallographic specimens, was used. The removed, circular-shaped area 10 mm in diameter was in the middle of the surface. For further X-ray diffraction measurements, the sample was sheltered by a nondiffracting plastic covering with a squareshaped hole of 5 mm × 5 mm. The depth profile of RS was studied for three samples with various cooling during grinding.
13 (MPa) 18 20 14 21 −18 17
± ± ± ± ± ±
2 2 4 2 2 3
23 (MPa) 9 −2 −2 7 −5 −3
± ± ± ± ± ±
2 2 2 2 2 1
12 (MPa) −24 39 −1 −12 34 12
± ± ± ± ± ±
6 6 12 4 7 5
from those obtained in the opposite direction, even if all geometrical conditions between the incident X-rays and the samples are maintained. From relation (1) it can be derived that shear stresses 13 and 23 are responsible for splitting in azimuths ϕ = 0◦ and ϕ = 90◦ , respectively. Both shear stresses 13 and 23 contribute to the splitting in ϕ = 45◦ . It was observed (Fig. 3) that the psi-splitting in azimuth ϕ = 0◦ diminishes with increasing distance from the surface; therefore, the stress component 13 decreases in its value. In all the performed measurements no splitting in a perpendicular direction to grinding was found, and, hence, the shear stress 23 was equal to zero in respect to the experimental accuracy. Various explanations for presence of shear stresses have been put forward. One of the most widely used interpretations [29,30] of this phenomenon ascribes the occurrence of shear components in the surface layers to anisotropy of multi-phase materials, gradients or coupled stress effects on the residual strains at the surface. A further explanation [31] is based on inhomogenities in the distribution of the Burgers vector of dislocations with strong density gradients from the surface. 4. Results Conditions for application of sin2 method were thoroughly explored. Firstly, the measurements of texture were performed; namely the unrolled spiral records of pole figure [32] were obtained. Secondly, backscattering Debye–Scherrer patterns contained continuous homogeneous diffraction rings and gave evidence of proper crystallite size. Since the process of stress relaxation cannot be omitted and so X-ray diffraction analysis was performed more than 2 months after the grinding. The complete tensor of macroscopic RS was evaluated for surfaces of six investigated samples. With respect to the decreasing dependency of effective penetration depth versus sin2 (Fig. 2), the calculation was carried out using only five tilts defined by sin2 = 0; 0.1; 0.2; 0.3 and 0.4, which corresponds to the inspected range of penetration depths from approximately 5 to 3 m. Moreover, as the calculated stresses represent mean values over the irradiated volume, the non-linearity in dependencies from Fig. 1 points not only to occurrence of shear stresses, but also of RS depth gradients within the penetration of primary beam. The results of surface RSs are shown in Tables 1 and 2; presented errors are standard deviations. The depth distributions of RSs were studied for both materials in three samples, cooled by ambient air, by liquid coolant, and by flow
3.1. Psi-splitting Evaluation of experimental data from measuring in positive and negative tilt (realised by rotating a specimen in the sample’s surface plane by 180◦ ) corresponds to different values of RS, which means that the stresses obtained in the grinding direction differ Table 2 Components of the surface stress tensor in ground samples of stainless steel M300 Coolant
11 (MPa)
Air 20 ◦ C Liquid Air 0 ◦ C Air −10 ◦ C Air −20 ◦ C Air −28 ◦ C
−7 −169 101 −171 −16 −154
± ± ± ± ± ±
21 25 30 21 12 18
22 (MPa) −262 −340 −180 −387 −211 −347
± ± ± ± ± ±
18 31 29 36 18 15
33 (MPa) 52 56 88 45 67 38
± ± ± ± ± ±
10 15 16 15 8 9
13 (MPa) −45 −30 30 23 44 37
± ± ± ± ± ±
3 5 14 3 8 4
23 (MPa) 3 −3 1 25 −15 8
± ± ± ± ± ±
22 18 18 15 22 15
12 (MPa) −3 2 1 1 5 3
± ± ± ± ± ±
3 4 9 8 4 6
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Fig. 4. Distribution of RS 11 and 22 in the samples made from low carbon 19MnCr5 steel ground in ambient air, with liquid cooling, and with cooled air at −28 ◦ C.
of cold air at −28 ◦ C. As the gradient of RS in the near-surface area of 100 m in depth has a pronounced impact on the surface quality, magnitudes of removing steps were chosen to reveal RS changes within this layer. All measurements were done in four azimuths ϕ = 0◦ , 90◦ , 180◦ and 270◦ . As psi-splitting was becoming less apparent at greater depths (Fig. 3), measurements at further depths (i.e. from 100 m onwards) were performed in only two azimuths ϕ = 0◦ and 90◦ . 5. Discussion 5.1. Shear stresses and psi-splitting Occurrence of a second phase, together with presence of tangential forces during machining, belongs to frequently mentioned conditions for creation of shear RSs. Whereas ground steels commonly exhibit shear stresses, it has been observed that even severely sheared single-phase materials do not. This leads to referring to shear stresses as oriented microstresses which cause peak shift, while non-oriented microstresses account for peak broadening. The model of shear stresses in multi-phase materials is, therefore, based on equilibrium condition or stress balance between phases, and presence of shear stresses in the investigated ␣-Fe phase would point to stress compensation in the remaining phases. Nevertheless, type of material and cooling condition have no effect on shear stresses depth distributions, thus, a comparatively high content of chromium in M300 steel has no evident effect on shear stress distributions. Another issue is the gradient of shear stress in the irradiated volume. If the shear stress was constant, the psi-splitting curves would form an ellipse with maximum width at about sin2 = 0.5 in [33]. The maximal width is shifted to higher values of sin2
majority of the investigated volumes indicating a steep gradient of shear stress even in shallow depth of 5 m. 5.2. Normal stresses and way of cooling The impact of various cooling environments on the final distribution of RS in the near-surface area is of vital importance from several points of view. Physical and chemical interactions, which take place at the surface and influence the component’s durability, and the crack propagation may be slowed down or even impeded by a favourable state of RS. Grinding generally produces a positive gradient of RS in the surface layers which means that stress increases in its value. It has been found that the difference between the surface value and the maximum in distribution is about 500 MPa. A frequent requirement of technologists is a compressively prestrained surface layer, when the surface RS is compressive and decreases in at least a 20-m region below the surface. This is an arduous task for grinding. As the results show, finish grinding can produce compressive stress on the surface, but prestraining is barely possible because of the generation mechanism of RS. The chosen materials are commonly ground and there is a clear difference in their chemical composition (i.e., 16% of chromium in M300), which might, or even should account for a difference in their behaviour with respect to both the nature of plastic deformation and cooling during grinding. Conduction of heat is vitally affected by the coefficient of thermal conductivity, which can change significantly even if small amounts of alloy in steel are present. For samples made from low carbon Mn–Cr steel stress components 11 and 22 equalize at a shallow depth of 10 m, while the same equalization can be seen in M300 in depths of approx. 100 m or even deeper (approx. 180 m for a sample cooled by liquid). The reason for such difference in behaviour might rest in either different
Fig. 5. Distribution of RS 11 and 22 in the samples made from stainless steel M300 ground in ambient air, with liquid cooling, and with cooled air at −28 ◦ C.
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plastic or hardness properties of the studied materials. Nevertheless, the main impact of various cooling environments on the state of RS is observed on the very surface and in the surface layers not deeper than 20 m; in low carbon Mn–Cr steel the depth distributions for depths greater than 20 m are the same with respect to the experimental inaccuracy. On the contrary, an apparent shift of RS distribution in corrosion-resistant M300 steel can be observed in the case of liquid cooling.
Acknowledgements
6. Conclusions
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• Measurements of residual strains on the surface of samples have proved that finish grinding causes anisotropic triaxial state of RS with psi-splitting of the dependences ε2 1 1 (sin2 ) in the direction of grinding and in the direction defined by azimuth ϕ = 45◦ . • As can be seen from Fig. 3, the shear component 13 diminishes as the psi-splitting vanishes. Using the quadric interpretation of tensor as a stress ellipsoid, it can be said that inclination of the principal axes of the stress ellipsoid in respect to the samples surface is decreasing with the increasing depth. • The absolute values of stress 22 on the surface are usually larger than 11 (the only exception being the sample of 19MnCr5 steel ground with cooled air at −10 ◦ C). • Cooling using liquid appears to be very effective in heat conduction from the surface as the diagonal components of the RS tensor are minimal (or the highest compressive). In this case all 11 are distinctly compressive and all 22 are among the maximal compressive stresses observed on all the surfaces. • Shear stresses are not influenced by the way of cooling. • Cooling with cold air from a Ranque–Hilsch vortex tube appears to be effective only for temperatures lower that −10 ◦ C when the diagonal stress components are rising in their values. • For the 19MnCr5 steel, the diagonal components 11 , 22 of macroscopic RS tensor increase from their surface values up to a maximum of about 250 MPa (Fig. 4), this state is reached in a depth of 80 m. From this point a decrease to a minimal level of about 50 MPa in a depth of 160 m is observed. With increasing depth, all three samples exhibit a further increase up to about 150 MPa. The explanation for this behaviour might possibly lie in the state of the samples before the actual grinding. • The maximum distribution of diagonal stress components 11 , 22 of the samples made from corrosion-resistant steel M300 varies according to the method of cooling. The maximum stress distribution of the liquid cooled sample is significantly higher than in the two other forms of cooling (Fig. 5). After reaching their maximum, the samples made from stainless steel do not exhibit any further increase in stress.
The research was supported by the Project No. 106/07/0805 of the Czech Science Foundation and by the Project MSM 6840770021 of the Ministry of Education, Youth and Sports of the Czech Republic. References
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Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
The impact of various cooling environments on the distribution of macroscopic residual stresses in near-surface layers of ground steels Z. Pala ∗ , N. Ganev Department of Solid State Engineering, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Prague 2, Czech Republic
a r t i c l e
i n f o
Article history: Received 5 December 2007 Received in revised form 30 June 2008 Accepted 2 July 2008 Keywords: X-ray diffraction analysis Residual stress distribution Shear stresses Grinding Cooling Electro-chemical polishing
a b s t r a c t Grinding often plays the role of final machining, and, therefore, its parameters significantly affect the properties of the treated surface. In this study, the state of surface residual stresses (RSs) and their depth distribution into the bulk is investigated with respect to various cooling environments during grinding. In order to acquire complete stress tensors, the sample surfaces were analysed using the X-ray diffraction technique. Since ε (sin2 ) dependences in grinding direction are non-linear and exhibit psi-splitting, the method proposed by Dölle and Hauk was used to evaluate the tensors of anisotropic triaxial state of RS. The effective penetration depth of Cr K␣ X-ray radiation into ferrous materials is approximately 4 m, and, therefore, removal of surface layers is necessary in order to pinpoint the distribution of RSs beneath the surface. The process of electro-chemical polishing ensures that the impact of material removal causes minimal or negligible mechanical and thermal distortions of the investigated state of stress. © 2008 Elsevier B.V. All rights reserved.
1. Introduction The grinding process can be employed at several stages of the manufacturing of machine components. The difference rests both in the modes and parameters of grinding. The depth of cut (thickness of removed layer) and wheel speed play a large role in determining whether the grinding is smooth enough in order to be the last step in the whole chain of manufacturing procedures. The goal of finish grinding is, above all, to achieve a high quality surface according to the requests of the customer. The appropriate choice of grinding parameters, material of grinding wheel abrasives and form of cooling has a relevant impact on the final quality. In order to obtain the proper conditions, it is necessary to take measurements of structural parameters of the surface. It is widely accepted that the state of residual stress (RS) on the surface and the near-surface area belongs among the most important parameters of surface quality. Macroscopic RSs may significantly affect the fatigue limit and wear life, and it could even increase the corrosion resistance. It has been shown [1] that, in general, compressive residual stresses in the material can favourably reinforce the dynamic strength by about 50%; on the other hand,
∗ Corresponding author. Tel.: +420 224 358 624; fax: +420 224 358 601. E-mail address: zdenek.pala@fjfi.cvut.cz (Z. Pala). 0921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2008.07.001
tensile RSs could reduce the dynamic strength by about 30%. Such advantageous effect of compressive RSs can be derived from mechanical model of counterbalancing, when the RSs mitigate the adverse effects of tensile load stresses [2] that occur during the service. Various techniques exist to determine RSs in materials; yet, out of the non-destructive methods, X-ray diffraction plays a prominent role because of its availability and accuracy. In combination with layer removal by electro-chemical polishing, stress gradients from the surface can be established and studied. The use of electrochemical polishing [3] can only be avoided if synchrotron radiation, which enables the variation of wavelength and hence adjustable penetration into material, is available. The conception of RS distribution in near-surface layers of a ground sample is based on the assumption of the inhomogeneous plastic deformation due to (i) mechanical interaction between the wheel and ground surface; (ii) equalization of temperature between the grinding zone and its environment [4]. In case of high grinding temperature (iii) phase transformation may occur, this would lead to an origination of transformational RS due to changes in crystal lattice [5]. The result of mechanical surface treatments with a tangential component, like milling, turning or grinding is inhomogeneous plastic deformation in the near-surface area resulting in RS due to the greater relaxation of this region compared to the bulk [6]. Plastic deformation of the surface layer inherently changes its
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Fig. 1. Dependences of 2 2 1 1 (sin2
201
) for low carbon 16MnCr5 steel ground with a liquid coolant.
volume which is reflected by a creation of elastic deformation in the adjacent zone [7], moreover, the plastically deformed layer acts as a barrier to full relaxation of elastically deformed areas of the material. This process of mechanical deformation (Herzian pressure) leads to compressive stresses on the surface, whose magnitude diminishes with increasing depth. Thermal RSs are created due to initial expansion of material in the grinding zone which is swiftly followed by a contraction owing to temperature levelling off between the grinding zone and its neighbourhood. It can be supposed that the ground surface itself embodies the point from which heat is conducted into the material. The amount of this heat ε, which is usually defined as a percentage share of the total heat output, is affected by a range of factors, among them the most decisive being the material of abrasives, the cooling of the surface, the grinding parameters, etc. The value of ε for conventional grinding conditions without cooling, for the corundum grinding wheel and common steels was established between 60 and 75% [8]. The quasi-steady temperature profile throughout the whole sample can be analytically computed according to the model of triangular heat source proposed by Jaeger [9] and Carslaw and Jaeger [10] if the ε is known. While the whole system strives to get into equilibrium the temperature profile dramatically changes over the course of time. The temperature on the very surface decreases rapidly, forming a barrier for cooling the near surface and bulk areas which are yielding to thermal expansion. Tensile RSs prevail on the surface only if thermal stresses surpass the yield stress of the material [4,5]; otherwise compressive stresses are present in the surface layer, balanced by tensile stresses in the bulk. Since the yield stress is strongly temperaturedependent, i.e., diminishes with rising temperature, tensile stresses might arise even at relatively moderate temperatures. The final shape of RS distribution is superposition of mechanical, thermal, and transitional residual stresses, all of which result from inhomogeneous processes. The aim of this study is a comparison of three manners of cooling during grinding from the point of view of macroscopic RS. X-ray diffraction measurements were performed to obtain stress tensors for surfaces and for the near-surface area of the ground samples.
The steel 16MnCr5 (DIN 17210) is suitable for case carburizing; it is often used in the automotive industry for parts with a required core tensile strength of 800–1000 N/mm2 and good wear resistance, like shafts, bolts and geared wheels [11,12]. The stainless martensitic chromium steel M300 (X36CrMo17) is corrosion-resistant with a chromium content of about 16%. It is used in moulds for chemically aggressive plastics and plastic abrasive fillers; it has outstanding corrosion and wear resistance [13] and a tensile strength of 800–950 N/mm. The square samples, 50 mm in dimensions, were 5.5-mm thick. All samples were first annealed at 550 ◦ C in an argon atmosphere for 2 h; the fall in temperature after annealing was gradual in order to rule out any additional thermal stresses. Two annealed samples, one from each material, were used for determining the unstressed lattice plane spacings. The finish surface grinding was conducted on the BPH 320 A face grinding machine. The identification label of the grinding wheel used designating its characteristics was 1 - 250 × 32 × 76 A98 60 K 9 V01–50 m s−1 ; just to highlight the significance of some symbols: the numbers 250 × 32 × 76 represent the dimensions and A stands for aluminium oxide (corundum) abrasive. The samples were fixed on a magnetic table, which was translating in respect to the grinding wheel rotation axis, and, hence, enabling the alternating processes of down-cut and up-cut grinding. The grinding conditions were as follows: the wheel speed: 35 m/s, tangential speed of table drift: 10 m/min, axial table drift: 1 mm per stroke, and thickness of removed layer: 0.02 mm. The grinding wheel was trued up after each sample in order to maintain constant grinding conditions.
2. Experimental 2.1. Samples Surface RSs and their gradients were studied in ground low carbon Mn–Cr steel 16MnCr5 and in high-carbon stainless steel M300.
Fig. 2. Effective penetration depth Te for Cr K␣ radiation into ferrous materials, -goniometer, = 80◦ .
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Fig. 3. Distribution of residual shear stress 13 in a sample from low carbon 16MnCr5 steel ground with cooled air at −28 ◦ C and dependences 2 2 1 1 (sin2 and at a depth of 50 m.
2.2. Cooling during grinding The mechanical interaction between the grinding wheel and workpiece is responsible for the increase in temperature in the area where friction takes place. A part of the emergent heat is conducted into the material and, taking into account inhomogeneous temperature fields, consequently thermal stresses arise. The creation of heat may even lead to thermal damage to the workpiece, which may severely reduce its fatigue and wear life [14]. A high level of tensile stresses may be included among thermal damages. Various cooling techniques are applied in order to conduct the heat away from the surface, and, thus, subdue tensile stress generation. Both gaseous and liquid cooling media are used. To evaluate the efficiency of cooling several parameters are measured. The distribution of RSs in the material is studied; the temperature during grinding may be measured either by thermocouple [15] or by CCD-based InfraRed imaging system [16]. Moreover, some coolants inherently also lubricate the grinding zone, which leads to a reduction of the friction between the grinding wheel and workpiece [17]. The level of lubrication can be estimated from the size of tangential and normal forces which are usually detected by piezo-electric dynamometers. In the experiment, an emulsion of water and synthetic fluid for machining operation Cimtech A31F was used as cooling liquid; the amount of incoming liquid being 5 l/min. The source of cooling air was a Ranque-Hilsch vortex tube [18]; four temperatures of air were used: 0, −10, −20 and −28 ◦ C. For comparison, one sample was ground without any cooling. 3. X-ray diffraction stress analysis The X-ray diffraction technique is a well developed and thus a widely used tool for measuring residual strains in polycrystalline materials. It is based on the assessment of lattice parameter. Changes of the lattice plane spacing dh k l are reflected by the peak position shifts in the X-ray diffraction pattern. The lattice strain εh k l is defined as a relative change of dh k l . The measured strain εh k l in the azimuth ϕ and in the tilt angle can be expressed as [19]: εhϕ k l = (ε11 cos2 ϕ + ε12 sin2ϕ + ε22 sin2 ϕ)sin2 +(ε13 cosϕ + ε23 sinϕ)sin2 .
+ ε33 cos2 (1)
If the strain is measured in six independent directions (ϕ, ), the complete symmetrical strain tensor comprising six components may be evaluated. The sin2 method stems from the proportionality of the measured strain εh k l to sin2 and is solely intended for the investigation of the biaxial stress state. There are several
) at the surface
limitations to the use of the sin2 method: (i) the texture of the investigated sample should not be pronounced, otherwise appropriate methods for evaluation of RS in textured material must be used [20], and (ii) the size of crystallites should be small (i.e., backscattering Debye–Scherrer patterns from the same irradiated volume should be homogeneous and continuous). Differentiating Bragg’s law, it can be found that the most convenient of Bragg’s angles are → 90◦ ; therefore {2 1 1} diffractions of ␣-Fe were investigated with Cr K␣ radiation (diffraction angle 2 ≈ 156◦ ) and an -diffractometer equipped with a scintillation detector. The goniometer was adjusted in reference to a strain-free reference specimen of ␣-Fe powder. The differential -method, when the azimuth is kept constant and the tilt is changing, was employed. Measurements were taken on the grinding direction (ϕ = 0◦ and 180◦ ), the transverse direction (ϕ = 90◦ and 270◦ ) and on the direction defined by azimuths ϕ = 45◦ and 225◦ ; corresponding to the positive (ϕ = 0◦ , 45◦ and 90◦ ) and negative (ϕ = 180◦ , 225◦ and 270◦ ) tilts. For each azimuth nine tilts defined by sin2 = 0; 0.1; 0.2; . . .; 0.8 were measured. The Bragg–Brentano focusing condition is fulfilled in case of -diffractometer only if the tilt is zero, and the irradiated surface, focus point of the X-ray tube and the incoming slot of the detector lie on the focusation sphere; otherwise, if the tilt is nonzero and the sample is flat, the experimental lay-out is in the so-called Bragg–Brentano parafocusing geometry. Although RSs are measured in higher 2, the deviation from Bragg–Brentano focusation when the surface is tilted (psi is nonzero) results in change of the measured diffraction profile shape. This would naturally require a misalignment correction; nevertheless, it was found out [21] that such correction would be statistically insignificant in the event of establishing the position of diffraction maximum as a centroid of diffracted doublet Cr K␣1 ␣2 . Hence this method was used after Lorentz’ polarization and temperature expansivity corrections [22]. The applied calculation of peak position does not render the misalignment correction unnecessary, but can minimize the sensitivity to deviations from perfect alignment as the integral centroid method is not as sensitive to line broadening as profile shape fitting parameters. The obtained courses 2 2 1 1 (sin2 ) exhibit psi-splitting for azimuths ϕ = 0◦ and 45◦ as shown in Fig. 1. method, Dölle and Hauk method (modified sin2 2 sin –sin (2 ) method) was implemented for calculation of the strain tensor from a+ and a− functions [23]. The calculation of stress tensor was done from the strain tensor by using the generalized Hooke’s law [24]: 1 ij = 1/2s2
εij −
s1 ıij εkk 1/2s2 + 3s1
,
(2)
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Table 1 Components of the surface stress tensor in ground samples of low carbon 19MnCr5 steel Coolant ◦
Air 20 C Liquid Air 0 ◦ C Air −10 ◦ C Air −20 ◦ C Air −28 ◦ C
11 (MPa) 105 −156 118 166 −2 −1
± ± ± ± ± ±
13 11 20 11 6 13
22 (MPa) −132 −318 −133 −101 −204 −217
± ± ± ± ± ±
16 11 14 11 7 10
33 (MPa) 61 39 70 60 70 57
± ± ± ± ± ±
8 6 9 6 3 6
where 1/2s2 = 5.76 × 10−6 MPa−1 and s1 = 1.25 × 10−6 MPa−1 are Xray elastic constants calculated according to the Eshelby–Kröner method [25] for measured ␣-Fe {2 1 1} diffraction planes. The evaluated RSs are mean values for the irradiated volume. Due to low penetration depth, the X-ray diffraction technique can be used only for surface layers of a few micrometers in thickness. The course of the effective penetration depth for diffractometer, Bragg’s angle = 80◦ and Cr K␣ radiation is shown in Fig. 2. It can be seen that the irradiated volumes vary markedly for different tilts. In order to confine information about RS to certain depth, computation of strain can be limited to tilts not larger than 45◦ or even less. For the case of conventional X-ray diffraction apparatus, investigation of stress depth profiles is carried out along with removal by electro-chemical polishing. During electro-chemical polishing the process of anodic dissolution [3] takes place. The anode is formed by the sample itself. The product of this process is a solution with high electrical resistance which is embedded into microscopic wells in the sample surface and preferential removal of roughness proceeds. However, layer removal does, by its nature, distort the original state of stress. A correction procedure proposed by Moore and Evans [26] and Sikarskie [27] exists for biaxial state of stress, which presumes that the whole surface area is being removed. This correction is often employed when shot-peened samples are investigated, but in this case of triaxial state of stress it would not be correct. An alternative attitude to this issue can exploit the finite element method: such computation [28] of stress redistribution due to the electro-chemical removal of layers has proved that distortions can be neglected if the removed area is in the centre of the sample and the removed volume is negligible with respect to the sample volume. For surface layer removal the LectroPol-5 by Struers, an apparatus for automatic, micro-processor controlled electrolytic polishing and etching of metallographic specimens, was used. The removed, circular-shaped area 10 mm in diameter was in the middle of the surface. For further X-ray diffraction measurements, the sample was sheltered by a nondiffracting plastic covering with a squareshaped hole of 5 mm × 5 mm. The depth profile of RS was studied for three samples with various cooling during grinding.
13 (MPa) 18 20 14 21 −18 17
± ± ± ± ± ±
2 2 4 2 2 3
23 (MPa) 9 −2 −2 7 −5 −3
± ± ± ± ± ±
2 2 2 2 2 1
12 (MPa) −24 39 −1 −12 34 12
± ± ± ± ± ±
6 6 12 4 7 5
from those obtained in the opposite direction, even if all geometrical conditions between the incident X-rays and the samples are maintained. From relation (1) it can be derived that shear stresses 13 and 23 are responsible for splitting in azimuths ϕ = 0◦ and ϕ = 90◦ , respectively. Both shear stresses 13 and 23 contribute to the splitting in ϕ = 45◦ . It was observed (Fig. 3) that the psi-splitting in azimuth ϕ = 0◦ diminishes with increasing distance from the surface; therefore, the stress component 13 decreases in its value. In all the performed measurements no splitting in a perpendicular direction to grinding was found, and, hence, the shear stress 23 was equal to zero in respect to the experimental accuracy. Various explanations for presence of shear stresses have been put forward. One of the most widely used interpretations [29,30] of this phenomenon ascribes the occurrence of shear components in the surface layers to anisotropy of multi-phase materials, gradients or coupled stress effects on the residual strains at the surface. A further explanation [31] is based on inhomogenities in the distribution of the Burgers vector of dislocations with strong density gradients from the surface. 4. Results Conditions for application of sin2 method were thoroughly explored. Firstly, the measurements of texture were performed; namely the unrolled spiral records of pole figure [32] were obtained. Secondly, backscattering Debye–Scherrer patterns contained continuous homogeneous diffraction rings and gave evidence of proper crystallite size. Since the process of stress relaxation cannot be omitted and so X-ray diffraction analysis was performed more than 2 months after the grinding. The complete tensor of macroscopic RS was evaluated for surfaces of six investigated samples. With respect to the decreasing dependency of effective penetration depth versus sin2 (Fig. 2), the calculation was carried out using only five tilts defined by sin2 = 0; 0.1; 0.2; 0.3 and 0.4, which corresponds to the inspected range of penetration depths from approximately 5 to 3 m. Moreover, as the calculated stresses represent mean values over the irradiated volume, the non-linearity in dependencies from Fig. 1 points not only to occurrence of shear stresses, but also of RS depth gradients within the penetration of primary beam. The results of surface RSs are shown in Tables 1 and 2; presented errors are standard deviations. The depth distributions of RSs were studied for both materials in three samples, cooled by ambient air, by liquid coolant, and by flow
3.1. Psi-splitting Evaluation of experimental data from measuring in positive and negative tilt (realised by rotating a specimen in the sample’s surface plane by 180◦ ) corresponds to different values of RS, which means that the stresses obtained in the grinding direction differ Table 2 Components of the surface stress tensor in ground samples of stainless steel M300 Coolant
11 (MPa)
Air 20 ◦ C Liquid Air 0 ◦ C Air −10 ◦ C Air −20 ◦ C Air −28 ◦ C
−7 −169 101 −171 −16 −154
± ± ± ± ± ±
21 25 30 21 12 18
22 (MPa) −262 −340 −180 −387 −211 −347
± ± ± ± ± ±
18 31 29 36 18 15
33 (MPa) 52 56 88 45 67 38
± ± ± ± ± ±
10 15 16 15 8 9
13 (MPa) −45 −30 30 23 44 37
± ± ± ± ± ±
3 5 14 3 8 4
23 (MPa) 3 −3 1 25 −15 8
± ± ± ± ± ±
22 18 18 15 22 15
12 (MPa) −3 2 1 1 5 3
± ± ± ± ± ±
3 4 9 8 4 6
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Fig. 4. Distribution of RS 11 and 22 in the samples made from low carbon 19MnCr5 steel ground in ambient air, with liquid cooling, and with cooled air at −28 ◦ C.
of cold air at −28 ◦ C. As the gradient of RS in the near-surface area of 100 m in depth has a pronounced impact on the surface quality, magnitudes of removing steps were chosen to reveal RS changes within this layer. All measurements were done in four azimuths ϕ = 0◦ , 90◦ , 180◦ and 270◦ . As psi-splitting was becoming less apparent at greater depths (Fig. 3), measurements at further depths (i.e. from 100 m onwards) were performed in only two azimuths ϕ = 0◦ and 90◦ . 5. Discussion 5.1. Shear stresses and psi-splitting Occurrence of a second phase, together with presence of tangential forces during machining, belongs to frequently mentioned conditions for creation of shear RSs. Whereas ground steels commonly exhibit shear stresses, it has been observed that even severely sheared single-phase materials do not. This leads to referring to shear stresses as oriented microstresses which cause peak shift, while non-oriented microstresses account for peak broadening. The model of shear stresses in multi-phase materials is, therefore, based on equilibrium condition or stress balance between phases, and presence of shear stresses in the investigated ␣-Fe phase would point to stress compensation in the remaining phases. Nevertheless, type of material and cooling condition have no effect on shear stresses depth distributions, thus, a comparatively high content of chromium in M300 steel has no evident effect on shear stress distributions. Another issue is the gradient of shear stress in the irradiated volume. If the shear stress was constant, the psi-splitting curves would form an ellipse with maximum width at about sin2 = 0.5 in [33]. The maximal width is shifted to higher values of sin2
majority of the investigated volumes indicating a steep gradient of shear stress even in shallow depth of 5 m. 5.2. Normal stresses and way of cooling The impact of various cooling environments on the final distribution of RS in the near-surface area is of vital importance from several points of view. Physical and chemical interactions, which take place at the surface and influence the component’s durability, and the crack propagation may be slowed down or even impeded by a favourable state of RS. Grinding generally produces a positive gradient of RS in the surface layers which means that stress increases in its value. It has been found that the difference between the surface value and the maximum in distribution is about 500 MPa. A frequent requirement of technologists is a compressively prestrained surface layer, when the surface RS is compressive and decreases in at least a 20-m region below the surface. This is an arduous task for grinding. As the results show, finish grinding can produce compressive stress on the surface, but prestraining is barely possible because of the generation mechanism of RS. The chosen materials are commonly ground and there is a clear difference in their chemical composition (i.e., 16% of chromium in M300), which might, or even should account for a difference in their behaviour with respect to both the nature of plastic deformation and cooling during grinding. Conduction of heat is vitally affected by the coefficient of thermal conductivity, which can change significantly even if small amounts of alloy in steel are present. For samples made from low carbon Mn–Cr steel stress components 11 and 22 equalize at a shallow depth of 10 m, while the same equalization can be seen in M300 in depths of approx. 100 m or even deeper (approx. 180 m for a sample cooled by liquid). The reason for such difference in behaviour might rest in either different
Fig. 5. Distribution of RS 11 and 22 in the samples made from stainless steel M300 ground in ambient air, with liquid cooling, and with cooled air at −28 ◦ C.
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plastic or hardness properties of the studied materials. Nevertheless, the main impact of various cooling environments on the state of RS is observed on the very surface and in the surface layers not deeper than 20 m; in low carbon Mn–Cr steel the depth distributions for depths greater than 20 m are the same with respect to the experimental inaccuracy. On the contrary, an apparent shift of RS distribution in corrosion-resistant M300 steel can be observed in the case of liquid cooling.
Acknowledgements
6. Conclusions
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• Measurements of residual strains on the surface of samples have proved that finish grinding causes anisotropic triaxial state of RS with psi-splitting of the dependences ε2 1 1 (sin2 ) in the direction of grinding and in the direction defined by azimuth ϕ = 45◦ . • As can be seen from Fig. 3, the shear component 13 diminishes as the psi-splitting vanishes. Using the quadric interpretation of tensor as a stress ellipsoid, it can be said that inclination of the principal axes of the stress ellipsoid in respect to the samples surface is decreasing with the increasing depth. • The absolute values of stress 22 on the surface are usually larger than 11 (the only exception being the sample of 19MnCr5 steel ground with cooled air at −10 ◦ C). • Cooling using liquid appears to be very effective in heat conduction from the surface as the diagonal components of the RS tensor are minimal (or the highest compressive). In this case all 11 are distinctly compressive and all 22 are among the maximal compressive stresses observed on all the surfaces. • Shear stresses are not influenced by the way of cooling. • Cooling with cold air from a Ranque–Hilsch vortex tube appears to be effective only for temperatures lower that −10 ◦ C when the diagonal stress components are rising in their values. • For the 19MnCr5 steel, the diagonal components 11 , 22 of macroscopic RS tensor increase from their surface values up to a maximum of about 250 MPa (Fig. 4), this state is reached in a depth of 80 m. From this point a decrease to a minimal level of about 50 MPa in a depth of 160 m is observed. With increasing depth, all three samples exhibit a further increase up to about 150 MPa. The explanation for this behaviour might possibly lie in the state of the samples before the actual grinding. • The maximum distribution of diagonal stress components 11 , 22 of the samples made from corrosion-resistant steel M300 varies according to the method of cooling. The maximum stress distribution of the liquid cooled sample is significantly higher than in the two other forms of cooling (Fig. 5). After reaching their maximum, the samples made from stainless steel do not exhibit any further increase in stress.
The research was supported by the Project No. 106/07/0805 of the Czech Science Foundation and by the Project MSM 6840770021 of the Ministry of Education, Youth and Sports of the Czech Republic. References