ASTA Beryllium Beam Exit WindowC. Baffes, 9/3/2010Beams Doc DB file: 4226https://beamdocs.fnal.gov/AD-private/DocDB/ShowDocument?docid=4226

Note: This work-in progress calculation investigated a Beryllium exit window for the ASTA beam lines. It was found that a Beryllium window would have marginal and uncertain fatigue performance. As such, this design path was abandoned and other graphite-based designs were pursued.

1 Summary of Options

1.1 Conventional Flat Window

Features:

Ti or Be foil brazed or e-beam welded into a flange

Pros:

Conventional design Low cost

Cons:

Ti: low conductivity leads to unacceptably large (>1000°C) temperature maxima right after the passage of a beam pulse.

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Be: expansion of heated material directly after the passage of a beam pulse is resisted by planar stiffness of the flat window. Unacceptably large compressive stresses arise.

1.2 DESY FLASH Window Design (M. Schmitz et al)

Features:

0.5mm Ti membrane sandwiched between thick graphite cups Ti provides vacuum tightness, graphite provides radial conductivity Beam swept over window with radius of 2cm, frequency of (?)

Pros:

Demonstrated to work (up to 900MeV/20kW) High factor of safety relative to pressure due to thick graphite section Failure mode likely graceful: gradual infiltration of pressure through graphite rather than “blowout”

Cons:

Beam sweeping required to minimize average temperatures, prevent graphite degradation Graphite introduces possibility of particulate contamination within the beamline Local water cooling required due to energy deposition in thick graphite section

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1.3 Domed Beryllium Window Design

Features:

Machined Be dome brazed into a CTE-matched Inconel 718 frame Domed shape reduces planar stiffness of the window and therefore reduces compressive stresses

caused by the beam

Pros:

Acceptable factors of safety in a comparatively simple design Can accommodate static (non-swept) beam

Cons:

Use of Be raises toxicity/mixed waste/safety concerns Failure mode would not be graceful: brittle fracture Backup window seems prudent Lack of fatigue data at relevant number of cycles (108-109)

o Data does support fatigue design at 107 cycles, but this only corresponds to ~550 hours of beam operation

o Replacing the window every few months would be unacceptable Extremely high cost: ~$10K per window + NRE

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1.4 “Fly-eye” Convoluted Window

Features:

Inconel 617 sheet provides strength and high temperature strength/creep resistance Copper-plating on both sides provides radial thermal conductivity Complex curvature (fly-eye texture) minimizes beam induced compressive stresses High surface temperatures would result in oxidation if exposed to air - best suited as a candidate for

a Be-window backup

Pros:

No toxic materials Window cost likely low (after expensive NRE/test phase) Ductile/tough material is likely forgiving

Cons:

Significant NRE required Tests of untried concept would be needed Copper coating is exercised plastically – may spall, flake or otherwise fail

2 Beryllium Dome Optimization

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3 Be Domed Window: Temperature and Stress Analyses

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4 Fatigue

4.1 Data DeficienciesA significant amount of fatigue data does exist for Beryllium. However, the available data suffers from the following deficiencies:

1. Lack of Data on Currently Available Grades: With the notable exception of S-200F (1), most fatigue data was generated in the 1960s, using grades of Beryllium with generally lower ductility than the grades that are currently available (2).

2. Lack of High-Cycle Data: No fatigue data has been found beyond 107 cycles. Due to the 5Hz pulse rate of the beam, we will accumulate 107 cycles in only 555 hours of beam operation, which could easily be accumulated within the span of a few months of calendar time.

3. Lack of High-Temperature Data: No elevated-temperature fatigue data has been found.

In order to deal with these deficiencies, the following approach has been followed

Problem 1 - Lack of Data on Currently Available Grades: The selected grade, I-220H, has the highest 0.2% yield strength (345MPa) and highest precision elastic limit (44MPa) of any available grade. Since the fatigue phenomenon is correlated with plastic deformation, we should expect favorable performance relative to other current and historical Beryllium grades.

Problem 2 - Lack of High-Cycle Data: In the absence of data, we are forced to extrapolate existing S-N curves. Most of these curves are essentially flat at 107 cycles (see Figure 1 and Figure 2 below), so we would predict little degradation in fatigue strength with increasing number of cycles. However, one poorly-documented S-N curve in the Brush Wellman Beryllium Design Brochure (3) showed a significant downward slope at 107 cycles (see Figure 3). We know little about the materials or conditions of this test. However, in an attempt to maintain conservatism, we use this curve for the extrapolation out to 109 cycles (see Figure 9), and to define the assumed slope of the I-220H bounding curves in the Goodman Diagram (see Figure 6 and Figure 7).

Figure 1: S-N Curves for Beryllium Sheet and Block (2).

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Figure 2: Fully Reversed (R = -1) S-N Curves for S-200F Block (1).

Figure 3: S-N Curves for S-200F and an unidentified HIP Block product (3), showing a negative slope at 107 Cycles

Problem 3 - Lack of High-Temperature Data: With increasing temperature, the tensile and yield strengths of Beryllium decrease in a well-correlated way, as can be seen in Figure 4. We assume that fatigue strength at temperature will be reduced by this same proportion. At a temperature of 250°C, which envelopes all temperature maxima expected on the window, we assume that the fatigue strength for a given number of cycles will be 79% of its room-temperature value.

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Figure 4: Temperature dependence of Beryllium Tensile Ultimate and Yield strengths (4)

It could be argued that looking at short-duration reductions in Ultimate Tensile Strength neglects the long-duration character of fatigue, and is therefore not appropriate. If so, a creep metric may be more appropriate. As before, a lack of data makes such a comparison difficult. However, (3) does contain a Larson-Miller Creep Curve for Beryllium Sheet.

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4.2 Fatigue Evaluation

4.2.1 Goodman Diagram and MethodPublished fatigue data is typically given for a single stress reversal ratio “R”, which is the ratio of the minimums stress within the loading cycle to the maximum. In order to compare the data to the actual R/σ fatigue loading conditions present in the window design, we have used a Goodman Diagram to interpolate fatigue strength at the relevant values of R. A simplified example of a Goodman Diagram is shown in Figure5.

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Figure 5: Fatigue life interpolation using a Goodman diagram

4.2.2 Fatigue Evaluation to 107 Cycles

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Figure 6: Goodman Diagram at 107 Cycles

Figure 7: Goodman Diagram at 107 Cycles – Compression Sector Only

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Figure 8: Goodman Diagram at 107 Cycles – Beryllium I220-H Failure Criteria Curves Only

4.2.3 Fatigue Evaluation to 109 Cycles

Figure 9: Extrapolation of HIP Block product R = 0.1 S-N curve (See Figure 3) to 109 cycles.

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Figure 10: Goodman Diagram extension to 109 Cycles

5 References1. Haws, Warren J. TM-778: Characterization of Beryllium Structural Grade S-200F. s.l. : Brush Welleman, 1985.

2. Floyd, Dennis R. and Lowe, John N. Beryllium Science and Technology, Volume 2. New York : Plenum Press, 1979.

3. Brush Wellman. Technical Brochure: "Designing with Beryllium". Undated.

4. US Department of Defense. MIL-HDBK-5H: Metallic Materials and Elements for Aerospace Vehicle Structures. 1998.

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