Rules for Handling
Large Borosilicate Honeycomb Mirrors

J. M. Hill, J. R. P. Angel, B. Olbert
Steward Observatory Mirror Lab

Columbus Project Technical Memo

UA-92-05

http://medusa.as.arizona.edu/lbtwww/tech/ua9205.htm

November 23, 1992

Introduction

This memo is intended to provide a summary of the proper strategy for safely handling large borosilicate honeycomb mirrors. Specific load cases should always be studied before handling a particular mirror, but the general rules for borosilicate honeycomb are stated here. Many of these rules also apply to other optics as well. The rules stated here are based on a combination of analytical analysis, finite element analysis and practical experience. This memo should be considered as a sensible set of guidelines and not an infallible authority.

We have set a goal for maximum local concentration of tensile stress in the blank due to support or handling of 100 psi (0.7 MPa). This number is well below the practical breaking strength of processed optics (1000 -- 2000 psi). Note that there is typically an order of magnitude difference between the average stress level and the maximum local concentration in the honeycomb blank. Based on 100 psi maximum stress, detailed finite element and engineerical analysis tell us that no location should carry a load of more than 2600 Newtons for each honeycomb rib intersection. The same stress threshold tells us that we should not allow temperature gradients larger than 5 C° across the blank. The appendices provide some of the background information for these rules.

At the risk of the stating the obvious, the answer for risk reduction is simple: BE CAREFUL!

Fundamental Rule

Subsidiary Rules for SOML Borosilicate Honeycomb

Mechanical Rules

Thermal Rules

Rules For Different Diameters

Rules Applied to All Mirrors

Incredibly Obvious Rules

Appendix A: Expected Internal Stress Levels

We expect the stress level in the finished blank to vary from about 0 to 20 nm/cm of birefringence. The residual stress is a combination of variations in the original E6 blocks and stress induced during annealing. The residual annealing stress puts the faceplates in compression and the ribs in tension. The prediction is based on annealing calculations and experience with the 3.5 meter blanks made by the same process. The stress is measured quantitatively with a Babinet compensator to measure the strain induced birefringence via the relative retardation technique. Measurements are made normal to the surface of the blank looking into the ribs. The peak measured stress in the three 3.5 meter mirrors was 73 psi, 87 psi and 65 psi respectively. The average stress values were typically half these values.

Appendix B: Failure Mechanisms

Failure occurs by extension of pre-existing flaws to a size critical for the applied stress field in the region around the flaw. The goal here is to determine the flaw size distribution and the stresses acting on the flaw, and then to set a fracture condition. The method is probabilistic unless you have a complete map of flaw sizes in your blank.

In most cases, failure probabilities are estimated from small sample strength tests. The Mirror Lab has done a substantial number of measurements on sample castings. Once the strengths are known, there are two ways to do mirror failure estimates. In the first method, the small sample strength distribution is scaled to the size of the mirror, and the failure probability is calculated at various stress levels. In the second method, the flaw size distribution is extracted from the strength data, and the probability of finding a critical flaw at various stress levels is estimated. The calculated strength of the mirror at low failure probabilities (10-6) can be several times smaller than the small sample strengths with no slow crack growth, and smaller still when allowances for slow crack growth are made.

The difficulty here is with the estimation procedure. The flaw distribution measured in small sample tests may not exactly represent the flaw distribution in the mirror blank. In cases where the sample strengths are several times higher than the mirror blank stresses, we must extrapolate far beyond the data range on the strength or flaw distribution curves. In spite of the problems, most people try to meet the conditions imposed by extrapolation.

Another design approach, called damage tolerance analysis, is sometimes used. Here we pick a mirror stress level, calculate the critical flaw size, and then try to hunt for flaws of this size or larger and get rid of them. We can also assume the existence of large flaws (like the observed rib cracks), calculate the critical stress level, and keep casting and handling stresses below this level. In our case (100 psi stress), the critical flaws would be large and hopefully easy to find. Calculations like this are important because flaws will extend with time by slow crack growth (in environments where water is present), so a flaw smaller than critical today may become critical 10 or 20 years from now.

Appendix C: Damage Control

Small cracks internal to the mirror blank would be treated by some combination of diamond grinding or acid etching to prevent propagation from stresses at the crack tip. This has been done successfully on small cracks in each of the 3.5 meter blanks. Surface defects up to a few centimeters or so could be repaired with a matching piece of E6 ground to fit and epoxied in place. This plug allows polishing over the defect without any problems. This technique was used on a 1 cm bubble in the WIYN 3.5 meter mirror.