Liquid impact erosion of single-crystal magnesium oxide

Wear 233–235 Ž1999. 39–50 www.elsevier.comrlocaterwear

Liquid impact erosion of single-crystal magnesium oxide M.J. Jackson ) , J.E. Field CaÕendish Laboratory, UniÕersity of Cambridge, Madingley Road, Cambridge, CB3 0HE, UK

Abstract The erosion of single-crystal magnesium oxide ŽMgO. by liquid impact is investigated using controlled liquid jet impacts produced by the Cavendish Laboratory’s multiple impact jet apparatus ŽMIJA.. The paper discusses the theoretical modelling of damage threshold curves which allows the investigation of the effect of changes in the damage threshold velocity ŽDTV. by changing material parameters such as flaw size, fracture stress, and fracture toughness. A model simulating the properties of single-crystal MgO is compared with experimental data using MIJA An attraction of using single-crystal MgO is that its cleavage and slip planes are well characterised and dislocation etching techniques are established. The early stages of deformation and fracture above the DTV are described. Comparison is made with erosion data of other infra-red transmitting materials. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Liquid impact; Erosion; Single-crystal magnesium oxide

1. Introduction When a droplet of liquid impacts a target the liquid behaves in a compressible manner generating the so-called ‘water-hammer’ pressure. This high pressure is responsible for most of the damage resulting from liquid impact and its magnitude is maintained while the edge of the contact area between the impacting liquid and the solid moves supersonically with respect to the shock wave speed in the liquid w1–4x. The essential features of the theory are summarised in a separate paper w5x, and are not duplicated here. There are various important implications from the theory of liquid impact. The first is that it is the initial stage of impact which generates the extreme pressures, which leads to damage. The second is that the precise geometry in the contact region is critical in determining the duration of the high pressures stage. For example, if a drop is flattened so that the effective radius is doubled then t , the duration of the compressible stage of impact, is similarly doubled. A key implication for laboratory testing of liquid impact is that liquid jets can simulate drop impact if the liquid jet is coherent and has a smooth, reproducible curved front profile. The dynamic criterion for threshold

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Corresponding author. Present address: Department of Engineering, University of Liverpool, P.O.-Box 147, Liverpool, L69 3BX, UK.

velocity for flaw growth, and thus strength loss, is given by Steverding and Lehrigk w6x as:

s 2t s constant,

Ž 1.

where s is the impact stress. It is possible to use this criterion to evaluate threshold velocity damage values for different particlerdrop sizes provided data are available for one particle or drop size. For liquid drop impact, the following equation is used w7,8x, V1

s

V2

d2

ž / d1

1r3

Ž 2.

where V1 is the threshold velocity for flaw extension for a drop of diameter, d1 , and V2 is the threshold velocity for a second drop of diameter, d 2 . There are three stress waves associated with the target when impacted where the waves represent the relative amplitude of particle motion. The two bulk waves Žlongitudinal or dilatational and shear or transverse. which propagate outwards into the target from the impact point have an attenuation of ry2 on the surface and ry1 in the bulk. The longitudinal is the fastest wave with a velocity C1. A second slower wave is the transverse wave with velocity, C2 , approximately two thirds the magnitude of C1 , with the exact ratio depending on the Poisson’s ratio. Note, that with an anisotropic material, such as single-crystal magnesium oxide, there would be two transverse waves. The

0043-1648r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 0 4 3 - 1 6 4 8 Ž 9 9 . 0 0 1 9 3 - 3

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M.J. Jackson, J.E. Field r Wear 233–235 (1999) 39–50

longitudinal wave is compressive as it travels outwards and with brittle materials has little effect on the damage pattern. However, when it reflects and changes phase to a tensile wave it can cause fracture. This is particularly important with small specimens. With thin plates, reflected waves from the rear surface can reinforce the front surface Rayleigh wave and cause bands of fracture. The analysis can be found in the works of Field w9x and Bowden and Field w1x. The third wave is the Rayleigh surface wave which interacts with the surface flaws that are intrinsic with brittle materials. The velocity of the Rayleigh wave is approximately 0.9C2 depending on the Poisson ratio of the material. The wave is confined to the surface and attenuates at a lower rate Ž ry1 r2 . compared to the surface bulk waves. The Rayleigh wave has both vertical and horizontal components and the depth to which the Rayleigh wave penetrates depends on the wavelength, which, in turn, depends on the impact velocity and the drop radius. The energy of the impact Žfor a single-element radiator. favours the Rayleigh surface wave with 67.4% of the total energy, the shear wave constitutes 25.8%, and the compression wave constitutes 6.9% of the total energy w10x. The role of the Rayleigh wave in causing circumferential cracking around the impact site is discussed by Field w9x and Bowden and Field w1x. In the rain erosion situation where most water drops have an average diameter of 2 mm or less, Rayleigh wave damage Žcircumferential damage. is the dominant mechanism leading to strength loss and damage. In this paper, experimental damage threshold curves use observations of circumferential damage as the mode of failure in singlecrystal MgO subjected to liquid impact.

2. Simulation of damage thresholds The damage threshold curve generated using the multiple impact jet apparatus ŽMIJA. is reproducible between samples of the same material. The absolute damage threshold velocity ŽADTV. of the sample material is related to the logarithm of the static fracture toughness, K IC , of the material w5,11x. However, the single-shot threshold and the remainder of the curve, although reproducible, does not seem to have a simple relationship to a single fundamental material property. A computer model was written that predicts the characteristic damage threshold velocity ŽDTV. curve for a material that uses parameters such as flaw size, fracture toughness, Young’s modulus, and Poisson’s ratio. The materials used to simulate the accuracy of the model include polycrystalline zinc sulphide and single-crystal magnesium oxide. Once the model was developed, it was possible to change various material properties Žsuch as critical flaw size., allowing investigation of how the DTV may change. This section presents the initial theoretical threshold curves for uncoated materials, and discusses the

implications for the shape of the experimental threshold curve. This section develops earlier attempts at modelling damage thresholds in materials subjected to liquid impact at the Cavendish Laboratory w12,13x and is applied to single-crystal materials where in-plane material properties are used to predict DTVs. 2.1. Damage threshold model The damage threshold incorporates three main sections: Ži. the mathematical approximation of the damaging Rayleigh wave which is related to the quasi-static calculations and the stress intensity at the tip of the crack, K S ; Žii. consideration of whether the flaw being sampled is static, or opening, and as an opening flaw may have a lower fracture toughness, k V , and therefore, be easier to extend than a static one; Žiii. the time dependency of the stress concentration at the flaw tip, k t , which can be considered as the response time to the passing wave, and relates strongly to the depth of the flaw. The three components are multiplied together, giving the dynamic stress intensity, K ID . If this value is greater than the fracture toughness, K IC , then the flaw will extend. When generating a threshold curve, up to 300 impacts may be directed onto a single site. If the impact velocity is greater than the ADTV of the material then the flaw will extend. It is believed that the DTV after 300 impacts will equate to the ADTV of the material, i.e., if a flaw starts to grow then it will be visible after 300 impacts. Therefore, a loop had to be generated that simulated the sequence of impacts, extending the flaw after each impact until it had grown beyond a critical length and became visible using an optical microscope. The damage threshold model performs a theoretical impact and repeats this until the flaw is greater than its critical length. The number of impacts required to extend the flaw beyond its critical length and reach a length of 100 mm was recorded. If the visible length of the crack is not reached after 300 impacts, then it is assumed that the impact velocity is lower than the ADTV of the material. The data generated are then plotted to produce a theoretical threshold curve. 2.2. Quasi-static stress intensity The quasi-static stress intensity is the intensity of the stress experienced at the crack tip assuming that the load is applied statically and across the whole length of the crack. However, it is not possible to provide a full stress analysis for a semi-elliptical crack in a varying stress field. The model uses the edge crack analysis of Hartranft and Sih w14x which states, K S s 2Y

CL

ž / p

1r2

CL

H0

s Ž z . Ž 1 q F Ž zrC L .

(Ž C y z 2 L

2

dz

Ž 3.

.

where Y is a dimensionless value which has a magnitude of approximately 2 for an edge crack, C L is the crack

M.J. Jackson, J.E. Field r Wear 233–235 (1999) 39–50

41

length, z is distance into the material, with z s 0 representing the impact surface. The integral was stored as a series of values in an array that were interpolated depending on the impact conditions to be simulated. Substituting s for zrC L , the function F Ž zrC L . is given by, F Ž s . s Ž1 y Ž s .

2

.

2

0.295 y 0.391 Ž s . q 0.769 Ž s . 6

y0.944 Ž s . q 0.509 Ž s .

8

4

Ž 4.

F Ž s . is equal to 0.295 at the surface of the sample and zero at the flaw tip ŽFig. 1.. The function K S has a discontinuity at the flaw tip when z s C L ŽFig. 2.. For the purpose of the model, the upper limit of the integral was changed to 0.99C L , which approximates to a real crack due to blunting. The integral was evaluated numerically by using the rectangular method of solution with integral steps of 1r10 000 of the total crack length. The s Ž z . function is the Rayleigh wave stress field over the length of the crack. In the case of liquid impact, the form of the stress, for single-crystal MgO with an in-plane Poisson’s ratio of 0.23, is,

sr Ž z . s s 0 Ž expy0 .839 k z y 0.58expy0 .4 k z .

Ž 5.

where s 0 is the magnitude of surface stress and k is the wave number of the stress pulse, which is given by Kolsky w15x as, ks

2p C 2 3CR RV

Ž 6.

where C is the over-driven shock wave speed, CR is the Rayleigh wave speed, R is the radius of the drop, and V is the impact velocity. The Rayleigh stress wave function for polycrystalline zinc sulphide was calculated using a Poisson’s ratio of 0.29. The Rayleigh wave contains both a shear and a longitudinal component. The wave is tensile at the surface and becomes compressive at a depth of approximately twofifths the magnitude of the Rayleigh wavelength which, for

Fig. 2. Plot of d K S rd z for the impact described in Fig. 1. The function tends to infinity at the flaw tip. The integral was evaluated using a rectangular method between 0 and 0.99 C L .

a 200 m sy1 impact on zinc sulphide, occurs at approximately 200 mm. The majority of the flaws in zinc sulphide are within the range 50–100 mm so the compressive regime will only act on the very deepest of flaws, possibly introduced by polishing. Indeed, polishing has a significant effect on the damage threshold of the material subjected to liquid impact. As the spatial decay of the Rayleigh wave is frequency dependent, it is necessary to determine its frequency for a given velocity. The Rayleigh wave is a single pulse and does not have a single well-defined frequency. With the original simulation, it was decided to simply use the fundamental frequency to avoid having to perform a Fourier transform on the roughly-shaped triangular pulse. At the release radius, the peak height of the simplified triangular wave pulse, by analogy with the Hertz theory, is suggested by Swain and Hagan w16x as,

smax s br CV

Ž 7.

where r CV is the water-hammer pressure and b is a function dependent on the Poisson’s ratio, n , of the target material, which is,

bs

1 2

Ž 1 y 2n .

Ž 8.

The decay of the magnitude of the Rayleigh wave is proportional to ry1 r2 . Therefore, the magnitude at any specified distance from the impact may be calculated from the initial impact conditions and the properties of the target material. For the purpose of the model the flaw under examination was at its most stressed point, the release radius. 2.3. Dynamic stress intensity Fig. 1. Plots of Rayleigh wave stress intensity, see Eq. Ž5., for an impact on ZnS at 200 m sy1 with a 100-mm flaw, and F Ž s . see Eq. Ž4.. The value 0 mm represents the surface of the sample.

The quasi-static section calculates the stress concentration applied at the flaw tip as if the impact load was static. However, the fact that the wave passes over the crack

M.J. Jackson, J.E. Field r Wear 233–235 (1999) 39–50

42

means that a time-dependent component is needed to describe the response of the flaw tip with time. The response of the flaw tip depends on the length of the crack, C L . The shorter the flaw, the sooner the flaw will respond to the surface wave, and as a consequence, the stress profile experienced by the flaw tip will be closer to that of the surface pulse. As the surface defect becomes longer, the response time increases and the stress profile at the tip becomes distorted with respect to that of the surface wave. The response time of the flaw tip, t , is given by:

ts

Ž 9.

4CR

As seen from Eq. Ž9. the faster the Rayleigh wave, the sooner the signal reaches the flaw tip. The stress intensity at the crack tip increases initially as t 1r2 , where t is the time after the impact, reaching a maximum of 1.25 times greater than the quasi-static value, K S , after t . The signal then decays in an oscillatory manner towards the quasi-static value as time tends to infinity. Owing to the short time durations involved with the impact, the model ignores the oscillations after t, and keeps a constant value of 1.25K S for t ) t . If the length of the approximate triangular Rayleigh pulse is T, then the crack tip experiences the full intensity of the impact if t - Tr2. If t is greater than this time, the stress will still be ramping in an ascending manner as the peak of the pulse passes. The dynamic response, k t , to the triangular pulse is segmented into six different intervals depending on the response characteristics of the material to the impact. The velocity of the opening flaw must also be considered in the threshold model. A modifying function is usually incorporated into the quasi-static function to take this into account. Freund w17x calculated the modifying function as, 1

ž

1q

Õmax s

(

2p E Br

Õ

Ž CR a y Õ .

/ž

1yg

Õ CR a

1r2

ž

1y

CL a

/

Ž 12 .

where B is a constant and C Lra is the ratio of the crack length to sample thickness. Robert and Wells w22x obtained a value for B, when a 4 C L , giving the maximum crack velocity, Õmax s 0.38

2 Ž 1.25p . C L

kV s

Dulaney and Brace w20x and Berry w21x calculated the maximum crack velocity as,

(

E

r

Ž 13 .

This is equal to approximately 0.6 CR , where the Rayleigh wave velocity is the maximum theoretical crack velocity, Field w23x has made measurements of maximum crack velocity for a number of materials, and shows that the maximum crack velocity in single-crystal magnesium oxide, for  1004 cleavage, is 5100 m sy1 . 2.4. Damage threshold curÕes Simulated damage threshold curves with material properties similar to uncoated zinc sulphide were generated and compared with the experimentally-determined threshold results w12x. The purpose of this was to show the accuracy of using the model with a brittle, polycrystalline material. The average flaw Žcalculated assuming a half-penny crack. was positioned at the release radius and the equivalent drop diameter was calculated for each jet velocity. Threshold curves were generated for a material with properties similar to uncoated zinc sulphide with an upper and lower limit of fracture toughness: 0.76 MPa my1 r2 ŽFig. 3.. The limits applied to fracture toughness indicate the variation in the properties of uncoated zinc sulphide tested at the Cavendish Laboratory. This is due to differences in the way the material is manufactured. The material with the higher fracture toughness gave the higher

Ž 10 .

/

where Õ is the current crack velocity and g is a constant related to Poisson’s ratio. When the flaw is static, k V is equal to 1 and when the crack is opening at the maximum theoretical velocity, the value of k V is 0, which is in agreement with Broberg w18x. The crack velocity is given by: K IC

2

ž ž //

Õ s Õmax 1 y

K ID

Ž 11 .

where K ID is the applied dynamic stress intensity, K IC is the fracture toughness of the impacted material, and Õmax is the maximum crack velocity w19x.

Fig. 3. Theoretical damage threshold curves for two different fracture toughness limits. Two values of K IC were chosen as the upper and lower limit of fracture toughness for this simulation. The theoretical damage threshold curves were generated using the properties of polycrystalline zinc sulphide.

M.J. Jackson, J.E. Field r Wear 233–235 (1999) 39–50

43

Fig. 4. Theoretical damage threshold curves produced using the computer model compared with experimental curves for polycrystalline zinc sulphide.

Fig. 6. DTV vs. flaw size for a material with the material properties of zinc sulphide and varying fracture toughness.

threshold velocity which is as expected. In comparison with the experimental curves ŽFig. 4., there was good agreement within the limits applied to the model with both the DTV Ž300 impacts. and the single-shot threshold velocity. This gives a reasonable level of confidence in determining differences in material performance when using this relatively simple impact model. A series of ADTVs were generated for a material with the properties of polycrystalline zinc sulphide by varying the fracture toughness and the critical flaw size w12x. The ADTV was calculated as the cut-off between crack growth and no crack growth. The fracture toughness of the material was varied between 0.5 and 5 MPa my1 r2 while the flaw size was varied from 10 to 200 mm. The ADTV increased linearly with increased fracture toughness for a constant flaw size ŽFig. 5.. Reducing the flaw size improved the ADTV considerably. This is to be expected as the quasi-static stress intensity over a smaller flaw is less than over a longer flaw. However, as the flaw size extended, the threshold velocity became constant, and when the flaw size became greater

than 100 mm, the ADTV was effectively independent of the critical flaw size ŽFig. 6.. Owing to the short duration and wavelength of the Rayleigh wave pulse, it should be expected that for very long flaws the DTV will not change as the whole flaw will not be fully stressed during the impact duration. This leads to the idea that a material with a poor surface finish, i.e., one with a longer average flaw size, will have a similar DTV. However, it should be mentioned that the lateral jetting aspect of the liquid impact was not incorporated into the model. Therefore, the longer flaws are subjected to Rayleigh wave stresses and not to hydro-static loading. The ADTV — log eŽ K IC . relationship is in agreement with the experimental data obtained by Seward w11x and Coad et al. w12x. A series of experiments were designed to compare the accuracy of the damage threshold model using the in-plane material properties associated with single-crystal materials. The damage threshold model was modified to produce a theoretical damage threshold curve using the material properties of single-crystal MgO. The Rayleigh stress wave function was changed to include an in-plane Poisson’s ratio value of 0.23 Žsee Eq. Ž5... The critical flaw sizes used in the damage threshold model to simulate the response characteristics of materials such as zinc sulphide, magnesium fluoride, sapphire, and silicon, were determined by bursting a number of disc samples and calculating their critical flaw sizes w12x. Owing to the lack of disc specimens, the critical flaw size for single-crystal magnesium oxide was calculated using Vardar and Finnie’s relationship w24x for quasi-static stress conditions,

ss

K IC

Ž 14 .

1.3'p c

Transposing Eq. Ž14. to find the solution for a half-crack length gives, Fig. 5. DTV vs. fracture toughness for a material with the material properties of zinc sulphide and varying flaw sizes.

cs

2 K IC

5.31 s 2

s 0.188

K IC

½ 5 s

2

Ž 15 .

44

M.J. Jackson, J.E. Field r Wear 233–235 (1999) 39–50

Substituting the respective values for single-crystal MgO, and multiplying by two, gives a critical crack length of 28.5 mm. This value was used in the computer model in order to calculate the ADTV of single-crystal MgO. The experimental DTV curve was generated using the MIJA: the damage threshold was detected by observing  1104 type cracks on the periphery of the central impact site, i.e., at the release radius.

3. Experimental 3.1. Materials Single crystals of MgO were supplied by Crystran ŽPoole, England. in the form of undoped high-purity single crystals. The specimens were prepared by Crystran for impact testing by cleaving and by mechanical and chemical polishing. The specimens were cleaved to size on  1004 planes. The specimens were then mechanically polished on one side of the specimen to remove cleavage steps. Chemical polishing was performed until mechanically-induced polishing dislocations were removed from the surface of the crystal. The surfaces were then oriented to within 58 of a  1004 plane. The impact face was denoted the Ž001. plane. The properties of MgO are listed in Table 1. 3.2. Rain erosion simulation The apparatus used to simulate rain erosion is the MIJA. For a full description, see Refs. w11,12x. The apparatus uses a two-stage pressure reservoir to accelerate a nylon piston into a titanium shaft positioned in the rear of a water-filled nozzle. The rapid insertion of the shaft into the nozzle forces a high-velocity jet of water from the orifice onto the sample which is located on a computercontrolled x–y stage. This arrangement allows the entire impacting process to be interfaced to a personal computer. The velocity of the jet is monitored by the computer. MIJA

Table 1 Properties of single-crystal magnesium oxide Young’s modulus, E ŽGPa. Poisson’s ratio Žin-plane., n Density, r Žkg my3 . Fracture toughness, K IC ŽMPa my1 r2 . Slip system Cleavage plane Water solubility Žmgr100 g water. Maximum crack velocity Žm sy1 . Knoop Hardness Žkg mmy2 . Ž001.²100: Ž001.²110: Ž110.²001: Ž110.²111: Ž110.²110:

249 0.23 3580 0.84 1104²110: 1004 0.62 5100 400 780–800 420 930 810

Fig. 7. Equivalent drop diameters for the 0.8-mm MIJA jet used in the study.

can produce a jet of water every 5 s with velocities in the range 80–600 m sy1 with a spread of less than 1%. Any chosen damage array is achieved by having the sample on a computer-controlled stage with a position accuracy of 10 mm. The damage caused by these water jets was evaluated and compared to that resulting from impacts with spherical water drops by Hand et al. w8x. Their data showed that the diameter of a water drop that gave the same damage pattern as a particular water jet diameter was dependent on the impact velocity. This is because the front of the jet is not a true hemisphere, but is slightly flattened, which means that at low velocities the jet gives the damage observed from a large water drop and as the velocity increases the equivalent drop diameter decreases ŽFig. 7.. The rain erosion resistance of a material is characterised by determining its ADTV. This is the velocity below which, for a given water drop size, the sample will never experience any damage regardless of the number of impacts to which it is exposed. Owing to the high accuracy of the MIJA jet velocity and positioning, this parameter can be simply obtained from a single sample. The sample Žtypically a 25-mm diameter disc. has up to 15 sites selected on its surface, each one allocated an impact velocity. Each site is initially impacted once at that velocity and inspected for damage using an optical microscope at 100 times magnification. The lowest velocity at which damage is observed after a single impact is recorded as DTV Ž1 impact., i.e., the single-shot threshold velocity, and the sample returned to MIJA so that each site can be impacted again. This process is repeated until a full DTV curve is obtained. A threshold curve for zinc sulphide is shown in Fig. 8 and shows that the curve becomes constant after, typically, 50 impacts. The intercept on the velocity axis after 300 impacts Ži.e., DTV Ž300 impacts.. is therefore very close to the ADTV of the material. The ADTV decreases as the impacting drop or jet diameter increases

M.J. Jackson, J.E. Field r Wear 233–235 (1999) 39–50

45

Fig. 8. A typical zinc sulphide damage threshold curve obtained from MIJA using a 0.8-mm diameter nozzle.

which is related to the number of flaws which can be sampled. 3.3. Detection of impact damage Impact damage was detected by inspecting the surface of impact using an optical microscope with the aid of Nomarski interference illumination. Nomarski interference illumination was also used to detect slip band movement in and around the centre of impact. Circumferential cracking was detected at the release radius using transmitted illumination in order to detect the appearance of cracks through the sample. 4. Results 4.1. Damage threshold curÕe for single-crystal magnesium oxide In order to simulate a theoretical DTV curve for singlecrystal MgO, it was essential to know the in-plane values of its fracture toughness. Measurements were made to one of the disc specimens to find the fracture toughness of single-crystal MgO. The method used involved indenting the sample using a Vickers’ diamond indenter and measuring the lengths of the cracks induced by applying a known load w25x in the crystallographic direction of measurement. The fracture toughness was found to be 0.84 MPa my1 r2 in the ²100: directions. Fig. 9 shows the comparison between the theoretical damage threshold curve produced by the computer model and the experimental damage threshold curve for single-crystal magnesium oxide using MIJA. It should be noted that the experimental damage threshold was determined by detecting evidence of circumferential damage at the release radius using transmitted illumination on an optical microscope. The single-shot threshold velocity from a 0.8 mm diameter nozzle was found to be 371 " 5 m sy1 , whilst the ADTV, i.e., DTV after 300 impacts, was found to be 245 " 5 m sy1 . It should be noted that for some velocities, the computer

Fig. 9. Theoretical damage threshold curve produced using the computer model compared with the experimental curve for single-crystal magnesium oxide. The theoretical single-shot threshold velocity is 512 m sy1 .

programme has rounded-up the number of fractional impacts. This explains the multiple data points at the two, three, and four impact points on the theoretical curve in Fig. 9. It should also be noted that the theoretical singleshot threshold velocity is greater than 400 m sy1 Žapproximately 512 m sy1 .. 4.2. Erosion of single-crystal magnesium oxide Figs. 10 and 11 show the influence of polishing grooves on surface damage. In general, if the polishing procedure is not properly controlled there will be damage left by the early stages of grinding and polishing with the larger-sized grits. This damage is often invisible since the fine-scale polishing debris Žthe so-called Beilby layer. fills the cracks. A polishing groove is a series of chatter marks with cracks opened by tension imposed by abrading particles. These cracks form small steps on the surface. If such steps

Fig. 10. Liquid impact damage on a 1004 face showing the effects of lateral jetting on the erosion of single-crystal MgO. Polishing cracks are evident and the erosion of material appears to follow ²110: and ²100: directions Žreflected illumination.. Impact conditions: V s 276 m sy1 , number of impactss150.

46

M.J. Jackson, J.E. Field r Wear 233–235 (1999) 39–50

Fig. 11. Liquid impact damage on a 1004 face showing the effects of lateral jetting of water on the erosion of single-crystal MgO. The letter A denotes the end of the erosion track Žreflected illumination.. Impact conditions: V s 276 m sy1 , number of impactss150.

impede the flow of water following liquid impact, material from these steps can be eroded w1,26x. Figs. 10 and 11 show typical examples. Note that in Fig. 10 there are two polishing grooves. One is much more eroded than the other and this is thought to be because it has its micro-chatter cracks Žcrystallographic in the case of single-crystal MgO. orientated to the flaw. Note that the polishing cracks are not the cracks predicted by the theoretical damage threshold model and are regarded as artefacts in that they are not the flaws which control the strength of well-polished MgO specimens. Referring to Fig. 10, the effects of lateral jetting of water are quite evident. The impact was performed on the  1004 face of single-crystal MgO Ždesignated the Ž001. plane.. The photograph shows the existence of two polishing cracks distributed randomly across the surface of the crystal which were created during the mechanical polishing process. The erosion track is situated radially approximately 6 mm from the centre of impact. Erosion damage occurs mainly in the ²100: directions with minor damage

Fig. 13. Circumferential damage pattern at the release radius adjacent to the impact site. The letter D denotes slip bands formed by the Rayleigh surface wave. Impact conditions: V s 370 m sy1 , number of impactss 3.

in the ²110: directions. Damage in the ²110: directions is in the form of half hexagon-shaped cracks dominated by the cubic nature of the crystal. By inspecting the nature of the damage in that direction, it appears that cracks in the material have formed an erosion track by removing the fractured material. This effect is not immediately apparent in the ²100: direction. Fig. 11 shows the effect of a polishing crack on truncating the flow of liquid. The erosion track has formed in the ²100: directions radially from the impact site. The crack has a step height of approximately 100 mm which appears to have diverted the flow of water in the directions shown in Fig. 11. The erosion track has been reduced in length and terminates a short length beyond the ridge of the polishing crack. The end of the erosion track is denoted by the letter A. The velocity of the liquid jet at impact was 276 m sy1 and the number of impacts was 150. 4.3. Rayleigh waÕe circumferential damage in singlecrystal MgO The nature of circumferential damage outside the release radius caused by Rayleigh surface waves is shown in

Fig. 12. Nature of circumferential damage viewed using reflected illumination. 1104 cracks occur in ²100: directions and are easily seen using transmitted illumination. The damage pattern indicates slip movement outside the area of impact in the form of slip bands ŽNomarski illumination.. Impact conditions: V s 370 m sy1 , number of impactss 3.

Fig. 14. Nomarski photograph showing the elliptical shape of the impact site. 1104 cracks were not evident when viewed using transmitted light. Impact conditions: V s 370 m sy1 , number of impacts on sites1.

M.J. Jackson, J.E. Field r Wear 233–235 (1999) 39–50

Fig. 15. Central impact site showing slip bands in the ²100: directions. A 1104 type crack can be seen in the centre of the impact site ŽNomarski interference.. Impact conditions: V s 350 m sy1 , number of impactss8.

Fig. 12. The  1104 type cracks occur in ²100: directions which are easily seen in transmitted light. Slip bands are evident in Fig. 12 and generally occur in the ²100: directions. Fig. 13 shows these slip bands adjacent to the centre of impact at the release radius. The damage sites are marked by the letter D. The impression at the centre of impact also shows slip band development predominantly in ²100: directions. Therefore, impact at higher velocities was thought to cause cracking at the centre of impact. The impact conditions were 370 m sy1 and the number of impacts registered as three. The approximate shape of the impact site is shown in Fig. 14. The shape is approximately elliptical implying anisotropic deformation behaviour. Slip band movement is in the ²100: directions, and no cracks were evident in the centre of impact. The impact was just below the DTV as there is no evidence of circumferential slip band development and fracture; impact conditions are one impact at 370 m sy1 . Increasing the severity of the number of impacts eventually led to a crack

Fig. 16. Central impact site as shown in Fig. 15 viewed in transmitted light. A 1104 type crack is seen complete with secondary ‘diffuse’ cracking about the centre of impact. The crack has propagated in the primary ²100: direction on a 1004 impact face. Impact conditions: V s 350 m sy1 , number of impactss8.

47

Fig. 17. Central impact site showing slip bands in the ²100: directions. Slip band development is in ²100: directions and is more pronounced at the higher velocities. Impact conditions: V s 405 m sy1 , number of impactss 2.

appearing at the centre of impact. Fig. 15 shows slip band development and the appearance of a crack in the centre of the impact site. Slip bands have again developed in ²100: directions. When viewed in transmitted light ŽFig. 16., the impact site shows a single  1104 type crack in the primary ²100: directions. About the centre of impact, the crack is surrounded by secondary ‘diffuse’ cracks which do not appear to have any principal orientation; impact conditions: impact velocity 350 m sy1 at eight impacts. Increasing the severity of the impact even further leads to more pronounced slip band formation at the centre of impact in the ²100: directions as shown in Fig. 17. When viewed in transmitted light ŽFig. 18., cracking at the centre of impact has occurred in all principal ²100: directions.  1104 type cracks are also accompanied by a large number of secondary ‘diffuse’ cracks which appear to follow ²100: directions. A small number of subsidiary cracks in the ²110: directions are evident. The velocity of impact was 450 m sy1 and the centre was impacted twice.

Fig. 18. Central impact showing 1104 type cracks Žcf. Fig. 17. and secondary ‘diffuse’ cracking predominantly in the ²100: directions although some subsidiary cracking occurs in the ²110: directions.

48

M.J. Jackson, J.E. Field r Wear 233–235 (1999) 39–50

5. Discussion 5.1. Damage threshold curÕes The damage threshold model uses the theoretical water-hammer pressure profile to approximate the shape of the Rayleigh wave pulse and then calculates the dynamic stress intensity factor at a given flaw by considering: Ža. the stress intensity factor of a stress pulse of that shape; Žb. the quasi-static stress intensity factor for a surface wave interacting with a crack of that particular length and; Žc. a modification factor to account for crack velocity. The model simulates the impacts from a 0.8-mm diameter MIJA jet and determines the extent of crack growth caused by each impact. If an estimate of ‘ visible’ crack size is made, then the MIJA threshold velocity for a given velocity can be predicted. The model has been used to predict the ADTV singlecrystal magnesium oxide as a function of the flaw size and the result is shown in Fig. 9 Žfor a fracture toughness of 0.84 MPa my1 r2 .. The predicted ADTV, i.e., DTV after 300 impacts is 280 m sy1 for a 0.8-mm diameter jet. Also shown in Fig. 9 is the experimental damage threshold curve for single-crystal magnesium oxide. The actual ADTV of the material is 245 " 5 m sy1 which is higher than the ADTV for other infra-red transmitting materials such as zinc sulphide, germanium, soda–lime glass, and CaLa 2 S 4 glass. Single-crystal MgO shares the same ADTV as magnesium fluoride. It should be noted that the damage threshold curves tend to stabilise at a constant velocity after approximately 50 impacts even though the severity of increasing the number of impacts contributes to a continuous loss of strength w12x. The insensitivity of the ADTV to the size of flaw Žbeyond a certain size. results from circumferential fracture being initiated by the Rayleigh surface wave. The surface wave decays exponentially with depth and becomes compressive at a depth of approximately two-fifths magnitude of its wavelength. For the impact velocities and jet size described in this paper, the depth is in the range 200–600 mm. The flaws are subjected to liquid impact stresses which decrease rapidly with depth, thus for long flaws, an increase in length will not increase the stress concentration at the crack tip compared to a static strength test. The flaw size is therefore usually a more crucial factor in the magnitude of fracture stress rather than in the ADTV. Therefore, this explains the accuracy of threshold velocity data Žcompared to strength data. in zinc sulphide which was discussed in Section 2.4. It is interesting to note that the experimental single-shot threshold velocity for single-crystal MgO, using a 0.8-mm diameter jet, was 371 " 5 m sy1 . In an earlier study on liquid impact of single-crystal MgO, Adler and James w27x observed that the single-shot threshold velocity for singlecrystal MgO was 450 m sy1 for approximate 1.6-mm diameter water drops. Using equivalent drop size diagrams

for a 0.8 mm diameter jet, the equivalent drop size of a jet travelling at 371 m sy1 is 3.42 mm. Eq. Ž2. was used so that a comparison can be made with the results of Adler and James w27x. Inserting the values into Eq. Ž2. gives the DTV as 478 m sy1 for an equivalent drop diameter of 1.6 mm Žwhere d1 is 3.42 mm, d 2 is 1.6 mm, and V1 is 371 m sy1 .. The MIJA equivalent velocity for a 1.6-mm drop diameter is within 10% of the DTV measured by Adler and James w27x, thus, confirming the accuracy of the MIJA. It is with this level of confidence that the ADTV of single-crystal MgO, using a 0.8 mm diameter jet, is 245 " 5 m sy1 . For an equivalent 2 mm drop diameter, the ADTV is 325 m sy1 for single-crystal MgO. 5.2. Erosion by lateral jetting When a shock wave accelerates at the free surface of the water droplet and release commences, small droplets are spalled away from the liquid surface. Their interaction with the target causes a high velocity sideways jet. The jetting of water at the surface has a velocity Vj which is faster than the impact velocity, V. Lateral jetting exploits any surface asperities which arise from differences in surface finish or damage introduced by the Rayleigh wave, resulting in material loss and further extension of the cracks ŽFig. 19.. The damaging effects of lateral jetting can clearly be seen with single-crystal magnesium oxide. Referring to Figs. 10 and 11, it is thought likely that mass loss is caused by the removal of an asperity that is subsequently dragged along the surface of the target by the flow of the jet. The half-hexagon shaped cracks that appear in the ²110: directions ŽFig. 10. may be caused by a lateral jet of water impacting a surface asperity, or a series of asperities, without removing that asperity, or asperities, and without the associated mass loss. However, the resulting force on the asperity, or asperities, may be enough to cause cracks to form in favourable crystallographic directions at points around the asperity where the surrounding material is in tension. 5.3. ObserÕations of surface damage The damage pattern observed after liquid impact of brittle materials is typically a series of discrete circumfer-

Fig. 19. The damaging effect of lateral jetting. The left hand side of the jet has been damaged by the Rayleigh surface wave. As lateral jetting traverses across the surface, it tears off asperities in its path.

M.J. Jackson, J.E. Field r Wear 233–235 (1999) 39–50

ential fractures around the undamaged central loaded zone. The fractures are caused by the Rayleigh surface wave emanating from the impact area w1x. The pressure pulses produced by liquid impact are intense because of the compressible behaviour of the liquid in the first stages of impact. The damage observed in single-crystal MgO outside the impact area was in the form of slip bands predominantly in ²100: directions until the material had reached its damage threshold limit. When the limit was reached,  1104 type cracks appeared in ²100: directions which were formed presumably by the interactions of  110445 8 slip planes, as observed by Adler and James w27x. Again, slip band development and crack formation is thought to be caused by the Rayleigh surface wave. Adler w28x had shown that substantial surface and near surface tensile stresses developed ahead of the shear wave in polycrystalline zinc sulphide just before the Rayleigh surface wave begins to develop. However, there was no evidence of sub-surface tensile cracking in the singlecrystal MgO samples. The cracks observed in the singlecrystal MgO samples were  1104 type in the ²100: directions, and not at trajectories associated with the shear wave. In some materials, repeated impact produces local failure on, or near the impact axis. Bowden and Brunton w26x found this with polymethylmethacrylate ŽPMMA.. In this case, the damage was located beneath the surface at a depth of about half the radius of the contact region R. This is where the Hertz theory for elastic contact would predict the maximum shear stress, and Bowden and Brunton suggested this as an explanation. However, for loading which is dominated by a stress wave this is unlikely to be the full explanation. Recent experiments by Obara et al. w29x show that sub-surface axial cracks in PMMA form when the release waves from the contact periphery interact giving a net tension. Interestingly, the release waves will also travel in the liquid giving cavitation when they cross. The nuclei for such cavities could be the air trapped at the interface during impact. When the cavities themselves collapse they could give peaks of pressure which damage the surface. A third mechanism for damage at or near the central axis with polycrystalline materials is by the action of compressive or shear loading which generates tensile failure at grain boundaries between grains depending on their orientation and anisotropy. Once a pit develops, hydraulic loading by trapped liquid can develop damage as shown by Field w9x. Central damage is likely to be less important than circumferential cracking in the rain erosion situation since it depends on multiple impacts on the same site; a situation which can be realised in the laboratory using MIJA but not by other techniques and only after very long exposures in the practical application. Central impact damage in single-crystal magnesium oxide initially occurs as slip bands move causing a ‘rippling’ effect to be seen using an optical microscope. As slip band development continues after repeated impact,

49

cracks begin to appear some distance above the DTV. Slip development leads to cracks predominantly in the w010x direction as shown in Fig. 16. As the severity of the impacts increases, cracking occurs in all principal ²100: directions. These cracks are thought to be due to the interaction of  110445 8 slip planes w27x. Although there are many explanations interpreting the effects of central impact damage in PMMA, the most likely explanation for central impact damage in single-crystal MgO is that hydrostatic compressive loading during impact enables subsurface slip bands to interact, i.e., shear interactions of slip planes. The slip planes which have a greater tendency to slip will do so thus causing the ‘rippling’ effect on the surface of the impact site. As the severity of impact continues,  1104 type cracks form due to the interaction of  110445 8 slip planes. This explanation was originally used by Adler and James w27x to describe circumferential cracks outside the impact region. It should be noted that Adler and James w27x did not observe cracks within the central impact region. However, they did notice that slip plane interaction did occur within the central impact region but without crack formation. Adler and James w27x concluded that slip development occurred on  110445 8 slip planes only. However, the present work observed the development of  1104 type cracks, which are produced by slip interactions on  110445 8 slip planes, and at higher velocities,  1004 type cracks are observed which are produced by slip interactions on  1104 90 8 slip planes. These secondary cracks appear as ‘diffuse’ subsidiary cracks which are associated with the principal  1104 type cracks ŽFig. 18.. Although parallels have been drawn with the work of Adler and James w27x, it should be noted that the movement of dislocations has not been investigated. Further studies will be carried out to confirm the role of dislocations in slip band interactions and how they contribute to failure of the material when subjected to repeated liquid impact.

6. Conclusions It has been shown that a DTV can be predicted for single-crystal MgO, and other infra-red transmitting materials, with great accuracy. A comparison was made with Adler and James’s w27x research on liquid impact of single-crystal magnesium oxide and found that the singleshot threshold velocity Žconsidering a 1.6-mm droplet diameter. was comparable although it must be borne in mind that the probability of opening a statistically larger flaw will be high which would give a substantially lower single-shot threshold velocity. This level of confidence in using MIJA to determine the DTV for a variety infra-red transmitting materials was used to find the ADTV of single-crystal MgO. Again, for a 2-mm droplet diameter, the ADTV of the material was found to be 325 m sy1 .

50

M.J. Jackson, J.E. Field r Wear 233–235 (1999) 39–50

Damage to the material due to lateral jetting is thought to be caused by a mixture of solid and liquid impact, i.e., a fast moving jet of liquid causing detachment of a surface asperity then further damage induced by that asperity scratching the surface as it is accelerated by the liquid jet. This type of damage is thought to contribute to the mass loss shown in Figs. 10 and 11. Circumferential damage in the form of slip band development in ²100: directions and the formation of  1104 type cracks is caused by the Rayleigh surface wave. The formation of these cracks is due to the interaction of  110445 8 slip planes. At much higher velocities, this effect is thought to cause slip band development and cracking in the central impact region by the action of shear loading on different slip planes. Further studies into the effect of dislocation interactions due to liquid impact will confirm these observations.

Acknowledgements The research was carried out with the support of D.E.R.A., Malvern. We thank Dr. J.A. Savage and Professor K.L. Lewis ŽMalvern., Dr. E.J. Coad and R.H. Telling ŽCambridge. for stimulating discussions, and R. Marrah for technical support. The principal author would like to thank Linda Jordan ŽLiverpool. for typing the manuscript, and Professor David Tabor, F.R.S., for constructive comments regarding the experimental work.

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