1.

Background

Multispectral zinc sulfide (MS-ZnS), also known as Cleartran^® or Waterclear^® zinc sulfide, is a polycrystalline ceramic window material with transparency from visible through mid-wave (3 to $5\mu \mathrm{m}$) to long-wave (8 to $12\mu \mathrm{m}$) infrared wavelengths and a cubic sphalerite crystal structure. It was discovered accidentally by C. B. Willingham at Raytheon Research Division in 1979 when he applied the newly available procedure of hot isostatic pressing to “standard” grade orange-yellow, translucent, chemical-vapor-deposited zinc sulfide, which is only useful in the long-wave infrared region.¹ He was hoping to remove traces of residual porosity and hexagonal phase. To protect the material from oxidation by traces of ${\mathrm{O}}_2$ in the high-pressure argon gas used for hot isostatic pressing, Willingham wrapped his samples in platinum foil. When he unwrapped the zinc sulfide after hot isostatic pressing, he was amazed to observe that the translucent colored material had been transformed into clear, colorless material now called multispectral zinc sulfide. It was later learned that platinum foil is essential to the chemistry that transforms yellow-orange zinc sulfide into clear, colorless zinc sulfide. If he had not wrapped the sample in platinum foil, MS-ZnS might never have been discovered.

MS-ZnS is a relatively soft ceramic with modest mechanical strength. It is easily damaged by sand abrasion or rain impact at aircraft speeds. In our application for MS-ZnS as an infrared sensor window for an airplane, the external surface of the window is in tension when the cabin pressure is greater than the external atmospheric pressure. In the absence of surface damage, the window lifetime is expected to be limited by the rate at which microscopic cracks in the material propagate to failure under the influence of tensile stress.

We are aware of one previous measurement of the slow crack growth rate in MS-ZnS (Cleartran^® from Morton International, Weeks Island, Louisiana, United States) in 1993.^2,3 Our MS-ZnS was manufactured by II-VI, Inc. (Saxonburg, Pennsylvania, United States). To characterize our window material, we measured the slow crack growth in coupons of II-VI MS-ZnS taken from the same two blank plates from which two aircraft windows were manufactured.

2.

Slow Crack Growth

When a flaw in a brittle material is subject to tensile stress in a reactive environment, bonds at the tip of the flaw can be chemically attacked and broken, resulting in the growth of the flaw.^4,5 For many materials including MS-ZnS, water, and, by extension, atmospheric humidity promote crack extension. The strength of a material measured in the absence of slow crack growth is called the inert strength (${\sigma }_i$). When measured in a reactive environment, slow crack growth occurs during the application of stress, so the failure stress (${\sigma }_f$) is less than the inert strength. For conservative window design, the slow crack growth rate is usually measured with test coupons immersed in liquid water to obtain an overestimate of crack growth rate in ambient humidity in the air.

The most common method for measuring the slow crack growth rate is dynamic fatigue. Test coupons are exposed to a series of constantly applied stress rates ${\dot{\sigma }}_a=d{\sigma }_a/dt$ while submerged in water (${\sigma }_a$ is applied stress and $t$ is time). The lower the stress rate is, the more time is needed to reach failure stress and the lower the failure strength is due to slow crack growth during the test. At high-stress rates, there is less time for slow crack growth to occur, so the failure stress is greater.

The slow crack growth rate ($v$) is generally described using two types of empirical equations:

ASTM C1368 and C1465 describe the use of dynamic fatigue testing to determine power law parameters $A^{*}$ and $n$.^6,7 For a constant applied stress rate ${\dot{\sigma }}_a$, the power law provides a relation of failure strength (${\sigma }_f$) to stress rate (${\dot{\sigma }}_a$) and inert strength (${\sigma }_i$) through Eq. (3), which is given as

Taking the logarithm of both sides of Eq. (3) produces a useful equation:

According to Eq. (4), the relationship between $\log ({\sigma }_f)$ and $\log ({\dot{\sigma }}_a)$ should be linear. We use linear regression to find the best-fit slope ($a$) and intercept ($b$). Crack growth parameters $n$ and $A^{*}$ in Eq. (2) are then found from the following relations, which are stated as

By contrast, the exponential law Eq. (1) does not have an analytical solution for the failure strength. However, Eq. (1) can be numerically integrated to calculate ${\sigma }_f$ for each experimental value of ${\dot{\sigma }}_a$ and trial values of parameters $v_o$ and $\beta$ in Eq. (1). In a separate paper, we describe a numerical integration procedure using an optimization algorithm to find the values of $v_o$ and $\beta$ that minimize the sum of squares of differences between calculated values of $\log ({\sigma }_f)$ and observed values of $\log ({\sigma }_f)$ for each experimental value of ${\dot{\sigma }}_a$.⁸

A window material might follow the exponential law Eq. (1) or the power law Eq. (2) over a wide range of stress intensity factors $K_I$. However, it is difficult to measure slow crack growth down to the low values of $K_I$ that apply to most of the service life of a window. In the absence of knowing whether the exponential law or the power law better represents the behavior of a given window material, the U.S. National Aeronautics and Space Administration prescribes that the more conservative exponential law be used to predict the service life.⁹ The window lifetime predicted by the exponential law can be one or more orders of magnitude less than the lifetime predicted by the power law fit to the same dynamic fatigue measurements.

3.

Experimental

3.4.

Fracture Toughness

Fracture toughness¹⁵ was determined on dry coupons in an atmosphere of ultrahigh purity ${\mathrm{N}}_2$ using the single edge V-notched beam (SEVNB) method.^16,17 The V-notch plane was perpendicular to the $5\mathrm{mm}\times 45\mathrm{mm}$ face of each flexure bar. A sharp razor blade with $1\mu \mathrm{m}$ diamond abrasive was placed into a straight saw-notch precut at the middle of a flexure test specimen to cut a sharp V-notch with its root radius typically $<10$ to $20\mu \mathrm{m}$ (Fig. 1). The ratio of sharp-notch length to test-specimen depth was in the range of 0.2 to 0.3. Fracture toughness was measured with a four-point flexure fixture with 20 mm-inner and 40 mm-outer spans. Test specimens with a length of 22 mm (instead of 45 mm) were measured by three-point flexure with a support span of 20 mm. A test rate of $0.2\mathrm{mm}/\min$ was applied to test specimens via the same test frame used for inert strength and dynamic fatigue testing. The sharp-notch length was measured with a digital microscope (Model VHX-S750E, Keyence, Japan) from the fracture surface of each broken test specimen based on a three-point measurement per ASTM C1421. Eleven test specimens were used in fracture toughness testing. Fracture toughness was calculated based on the formulas given in ASTM C1421.

Fig. 1

V-notch generated on a flexure specimen for measuring fracture toughness (notch root $\text{radius}\sim 20\mu \mathrm{m}$). The marker bar is 2 mm.

4.

Results

Table 1 summarizes measured values of elastic constants, hardness, and density.

Table 1

Elastic constants, microhardness, and density of MS-ZnS.

4.1.

Inert Strength Weibull Parameters

All disks for inert strength and dynamic fatigue failed within the load ring diameter at surface or subsurface damage associated with processing or from surface/subsurface grains. Figure 2 shows Weibull plots for the inert strength of uncoated and antireflection-coated MS-ZnS in dry nitrogen. The maximum likelihood method in ASTM C1239²³ was used to compute Weibull parameters in Table 2.

Fig. 2

Inert strength Weibull distributions for uncoated and antireflection-coated MS-ZnS.

Table 2

Inert strength Weibull parameters.

Weibull parameters	Uncoated MS-ZnS	Coated MS-ZnS	Cleartran2 1993 data
Weibull modulus $m$ (unbiased)	4.68	5.25	5.93
Characteristic strength ${\sigma }_{\theta }$ (MPa)	124.1	106.9	95.8
Scale factor ${\sigma }_o$ (MPa)	181.9	149.4	121.3
Coupon effective area $A_e$ (${\mathrm{cm}}^2$)	6.00	5.78	4.04
Stress at 50% failure probability	114.7	99.7	90.4

Curves in Fig. 2 were fit to the Weibull equation

Eq. (8)

$$P_f=1-e^{-{\left(\frac{\sigma }{{\sigma }_{\theta }}\right)}^m},$$

where $P_f$ is the probability of failure, $\sigma$ is the applied stress, ${\sigma }_{\theta }$ is the characteristic strength, and $m$ is the Weibull modulus. The form of the Weibull equation that allows for area scaling is

Eq. (9)

$$P_f=1-e^{-\left(\frac{A_e}{A_o}\right){\left(\frac{\sigma }{{\sigma }_o}\right)}^m},$$

where $A_e$ is the effective area in tension, $A_o$ is the unit area ($1{\mathrm{cm}}^2$) for unit cancelation, and ${\sigma }_o$ is the Weibull scale factor, which is the characteristic strength for a $1{\mathrm{cm}}^2$ area in uniaxial tension. The relation between the characteristic strength ${\sigma }_{\theta }$ and the Weibull scale factor ${\sigma }_o$ is

Eq. (10)

$${\sigma }_o={\left(\frac{A_e}{A_o}\right)}^{1/m}{\sigma }_{\theta }.$$

The effective area $A_e$ for a disk in an equibiaxial flexure test is²⁴

Eq. (11)

$$A_e=2\pi r_l^2\{1+\frac{44(1+\nu )}{3(1+\mathrm{m})}\frac{5+\mathrm{m}}{2+\mathrm{m}}{\left(\frac{r_s-r_l}{r_s{r}_d}\right)}^2[\frac{2r_d^2(1+\nu )+{(r_s-r_l)}^2(1-\nu )}{(3+\nu )(1+3\nu )}\left]\right\},$$

where $\nu$ is Poisson’s ratio, $m$ is the Weibull modulus, $r_l$ is the load radius, $r_s$ is the support radius, and $r_d$ is the disk radius.

We display the strength of both uncoated and antireflection-coated material in Fig. 2 because there are few examples in the literature showing the effect of coating on mechanical strength. For both the strength and the rate of slow crack growth (presented in the Sec. 4.2), we find only small differences between coated and uncoated material. This behavior is not unexpected but is rarely investigated.

The mean strength of 30 uncoated disks of MS-ZnS was 113.5 MPa with a standard deviation of 27.9 MPa. The mean strength of 30 coated disks was $98.7\pm 21.3\mathrm{MPa}$. The coated disks are 87% as strong as the uncoated disks for this particular anti-reflection coating. The difference in strength is statistically significant at the 97% confidence level in a two-tailed $t$-test for Gaussian statistics.

4.2.

Dynamic Fatigue Slow Crack Growth Parameters

Figure 3 is a graph of Eq. (4) showing 150 dynamic fatigue measurements (circles) of uncoated MS-ZnS at five stress rates spanning four orders of magnitude. The solid line is the least-squares linear fit to the 150 points. Tables 3 and 4 give observed failure stresses and the Weibull modulus for each set of 30 measurements at each stress rate.

Fig. 3

Dynamic fatigue measurements of optically polished MS-ZnS disks in distilled water at 21.8°C to 24.6°C. Round points are uncoated samples. Square points are antireflection-coated samples. The solid straight line is the least-squares fit (the same as the power law fit) to the uncoated disks. The dashed curve is the exponential law fit to uncoated samples.

Table 3

Dynamic fatigue and inert strength data for uncoated MS-ZnS (2021).

	Inert strength	Dynamic fatigue	Dynamic fatigue	Dynamic fatigue	Dynamic fatigue	Dynamic fatigue
	σ (MPa)	10  MPa/s	1  MPa/s	0.1  MPa/s	0.01  MPa/s	0.001  MPa/s
	51.67	53.71	43.58	34.54	27.61	26.88
	62.63	56.24	44.18	37.91	31.40	27.48
	65.28	56.64	47.21	40.80	32.62	28.29
	77.95	59.60	48.81	41.36	33.26	29.77
	86.69	62.30	48.88	41.88	36.97	31.56
	88.54	62.99	52.54	42.62	37.06	31.66
	94.02	63.28	54.88	42.64	38.84	32.37
	94.33	64.31	55.08	44.12	40.76	33.78
	98.83	64.61	55.28	44.94	40.83	33.90
	102.32	66.20	56.45	45.35	41.00	36.68
	103.64	66.88	57.07	45.38	41.91	37.01
	109.51	67.28	58.44	45.74	42.34	40.36
	111.43	68.39	60.41	46.62	44.16	41.97
	111.56	68.93	63.50	47.86	46.05	42.74
	113.89	69.11	64.82	49.59	46.48	43.61
	114.51	73.45	65.40	50.35	48.13	43.96
	116.31	74.66	66.42	51.26	51.34	44.32
	119.26	75.99	69.73	51.61	52.09	45.81
	119.62	76.76	70.30	62.42	52.56	46.38
	128.90	77.56	71.13	64.36	53.02	47.05
	131.87	79.74	73.00	65.00	53.51	47.52
	135.39	80.60	75.02	66.76	55.18	48.43
	135.52	83.18	75.59	67.15	56.33	49.29
	137.26	84.93	76.43	67.96	56.65	50.31
	137.90	90.59	79.82	69.38	58.00	50.89
	145.96	90.75	80.91	69.44	58.72	50.96
	148.06	94.51	84.80	70.95	63.24	51.92
	152.42	97.90	85.10	71.08	63.75	55.23
	155.44	104.63	87.97	72.73	67.76	59.62
	155.44	108.83	89.58	73.01	68.18	60.23
Mean	113.54	74.82	65.41	54.16	47.99	42.33
Std. dev.	27.92	14.40	13.49	12.47	11.00	9.49
Weibull $m$	4.68	5.14	5.25	4.69	4.72	4.91

Table 4

Dynamic fatigue and inert strength data for coated MS-ZnS (2021).

	Inert strength	Dynamic fatigue	Dynamic fatigue
	σ (MPa)	10  MPa/s	0.01  MPa/s
	45.49	41.64	29.45
	57.88	44.90	32.01
	68.22	47.23	32.84
	76.92	47.63	33.44
	77.45	51.64	34.06
	83.75	52.15	37.97
	86.60	53.45	38.37
	88.42	55.10	39.44
	88.83	56.37	40.24
	90.99	57.45	42.01
	91.72	57.60	42.93
	91.80	61.73	46.80
	93.81	62.21	46.85
	95.08	62.82	47.21
	96.22	64.68	49.79
	99.29	66.41	49.82
	100.43	66.65	49.96
	101.93	68.28	50.28
	103.32	68.92	50.42
	104.92	73.01	51.33
	106.79	73.34	52.65
	108.34	74.02	56.67
	117.10	83.87	57.28
	120.01	85.91	59.12
	122.68	89.85	59.76
	124.60	90.48	64.48
	124.74	92.52	64.56
	126.04	93.23	66.74
	131.41	98.50	74.67
	134.90	99.53	75.05
Mean	98.66	68.04	49.21
Std. dev.	21.34	16.87	12.32
Weibull $m$	5.25	4.24	4.17

Power law slow crack growth parameters $n$ and $A^{*}$ in Eq. (2) were determined from the straight line in Fig. 3. From slope $a=0.0639$, intercept $b=1.800$, and inert strength ${\sigma }_i=114.7\mathrm{MPa}$ (Table 2), the parameters $n=14.65$ and $A^{*}=0.0769\mathrm{m}/\mathrm{s}$ are found with Eqs. (5) and (6).

Best-fit exponential law crack growth parameters $v_0=3.02\times {10}^{-14}\mathrm{m}/\mathrm{s}$ and $\beta =43.64{(\mathrm{MPa}\sqrt{\mathrm{m}})}^{-1}$ for Eq. (1) were calculated by fitting the same 150 points in Fig. 3 by numerical integration with an optimized procedure to rapidly locate the optimum crack growth parameters.⁸ The dashed line in Fig 3 is the exponential crack growth law fit to the 150 points calculated from $v_0$ and $\beta$ by the integration of Eq (1) at each of the five stress rates. Over the measured stress rate range, the power and exponential laws fit nearly identically.

5.

Discussion

To the best of our knowledge, the only other dynamic fatigue measurements of MS-ZnS appeared in a 1993 report,² the results of which are displayed in Figs. 4 and 5 and Tables 5 and 6. Results were provided to us and reported in our 2017 paper.³ The 1993 study used Morton Cleartran^® zinc sulfide, which is made by the same general process as II-VI MS-ZnS. Five stress rates were employed with 4-point flexure specimens immersed in water. Inert strength was measured with bars immersed in liquid nitrogen to prevent slow crack growth.

Fig. 4

Dynamic fatigue measurement of Morton Cleartran^® zinc sulfide 4-point flexure bars immersed in water at 21°C.² The least-squares slope and intercept are fit to all points in either four of the stress rates or all five stress rates. Inert strength measured in liquid nitrogen was ${\sigma }_{\mathrm{i}}=90.4\mathrm{MPa}$ (50% probability of failure on the Weibull curve). The study employed ASTM C1161²⁵ type C bars with dimensions of $6\mathrm{mm}\times 8\mathrm{mm}\times (90\mathrm{mm}\text{or}100\mathrm{mm})$ with 40 mm load span and 80 mm support span.

Fig. 5

Comparison of 2021 and 1993 ZnS slow crack growth velocities.

Table 5

Dynamic fatigue and inert strength data for Cleartran® zinc sulfide (1993).

Table 6

Slow crack growth parameters derived from dynamic fatigue studies.a

Comparison of the 2021 and 1993 full data set crack growth velocities in Fig. 5 shows significant disagreement. At a stress intensity factor of $K_I=0.25\mathrm{MPa}\sqrt{\mathrm{m}}$, which is representative of operating conditions for an aircraft window, the 1993 exponential law predicts a crack growth rate $\sim 200$ times lower than that for the 2021 data and a widow lifetime that is $\sim 200$ times greater. We had no reason to expect that the slow crack growth rate would be substantially different in the 1993 and 2021 materials. They are both made by the same process of chemical vapor deposition followed by hot isostatic pressing while wrapped in platinum foil. Their optical and elastic properties and fracture toughness are equal within measurement uncertainty.

This disagreement in the slow crack growth rate led us to examine the 1993 data more carefully. In Fig. 4 the average failure stress at the highest stress rate of $82.7\mathrm{MPa}/\mathrm{s}$ is 67 MPa. The average failure stress at the second-highest stress rate of $7.9\mathrm{MPa}/\mathrm{s}$ is 71 MPa. The strength at higher stress rates should be greater than the strength at lower stress rates because there is 1/9 as much time for slow crack growth to occur at the higher stress rate. We speculate that the highest-stress-rate data might be invalid, perhaps because the test machine could not implement the highest stress rate or measure stress accurately at the highest stress rate.

Figure 4 shows an alternate interpretation of the 1993 data in which the highest stress rate is discarded. The dynamic fatigue fit shown by the dashed line has a greater slope than the fit to the full data set. The exponential law derived by omitting the highest-stress-rate data is shown in Fig. 5 and is closer to the 2021 exponential law. At the service stress intensity factor $K_I=0.25\mathrm{MPa}\sqrt{\mathrm{m}}$, the 1993 and 2021 window lifetime predictions differ from each other by a factor of 10 rather than a factor of 200 predicted by the full 1993 data set.

6.

Summary

Mechanical properties necessary to design a sensor window were measured on multispectral zinc sulfide. Inert strength was characterized by Weibull parameters describing the strength distribution. Dynamic fatigue data were fit using both power and exponential crack growth laws. Results were compared with measurements made in 1993 on Cleartran^® ZnS, which is made in essentially the same manner as MS-ZnS. The observed slow crack growth velocity in the present work is one or two orders of magnitude greater than previously reported.