Titanium

Uses

Titanium alloys are used for:

  1. Resonators with high stress.
  2. Resonators that must meet biological compatibility requirements (e.g., for surgical tools or implants).
  3. Resonators that must have moderate resistance to impact, wear, and cavitation erosion.
  4. Resonators that must resist chemical attack.

Applications include medical (surgical), plastic and metal welding, liquid processing, and food packaging and cutting.

Properties

Orthotropic considerations

Titanium is orthotropic which means that the material properties depend on the direction in which the material is tested with respect to the grain direction. The grain directions are commonly labeled as longitudinal L (i.e., parallel to the grain), transverse T (also called long transverse LT), and short transverse ST. See the following figure from Bowen (p. 1273).

Bowen (p. 1272) lists the following properties for this material. Note the substantial dependence on the test direction.

Table notes:

  1. The material is Ti‑6Al‑4V, forged and annealed, 235 mm wide x 57 mm thick .
  2. E = Young's modulus.
  3. The thin wire wave speed C0 is calculated as √(E/ρ) where the assumed density ρ is 4430 kg/m3. These C0 values were not included in the original table.
  4. The fatigue strength is approximate at 107 cycles.

For titanium Young's modulus and the wave speed depends on the following factors:

  1. The direction of vibration with respect to the grain direction (see the table).
  2. The position of the raw material along the length of a bar.
  3. The heat from which the sample was produced. Variations may also occur from different samples of the same heat (see below).
  4. The raw stock type (rod, bar, sheet, or plate).
  5. For rod material, the raw stock diameter (see below).

Thus, because the wave speed or modulus of titanium may not be precisely known, the tuned length of a titanium resonator will not be entirely repeatable and may not be precisely predicted, even using computer simulation.

Loss (Q)

Variation with grain direction

Limited experimental data indicates that the loss depends on the vibration direction relative to the grain.

Fatigue characteristics

Titanium alloys have an endurance limit (stress) below which the material will have infinite life. However, the exact value of this endurance limit is somewhat difficult to determine. See the discussion below for Ti‑6Al‑4V.

Ti‑6Al‑4V (ASTM grade 5)

When a titanium alloy is required, Ti‑6Al‑4V (6% aluminum, 4% vanadium) is most commonly used, in part because it is widely available. Also, because this alloy is widely used for non-ultrasonic applications (particularly aerospace), a huge knowledge base has been compiled. Ti‑6Al‑4V is approved in the U.S. and other countries for ultrasonic surgical devices.

Note that Ti‑6Al‑4V only designates the chemical composition. Some properties may vary considerably depending on factors such as grain direction, heat treatment, processing, etc.

Loss (Q)

As indicated by the following table, Ti‑6Al‑4V has the lowest loss (highest Q) in the annealed condition. (The raw stock for all of these tests is believed to be cylindrical.)

The Wuchinich material was heated to 940 °C (1725 °F) for one hour and then water quenched, giving a Rockwell C hardness of 65 (p. 4).

Modulus and wave speed - variation with diameter

Cylindrical stock

For annealed rod stock, various tests by Culp indicate that Young's modulus depends on the material's raw stock diameter (i.e., the diameter of the raw material from which the horn was machined).

The above data were mainly generated by analyzing a horn design with FEA and then adjusting Young's modulus until the FEA frequency agreed with the actual horn's measured frequency. The confidence in the results is reasonably high so the data scatter must likely be attributed to variations in the titanium material. This is a known problem with titanium. (See the further discussion below.)

Because the data scatter is fairly large, the trend indicated by the regression line is not absolutely confirmed (as indicated by the low coefficient of determination R²). However, if true then the thin–wire wave speed and the tuned length will be affected.

Using the regression equation for Young's modulus from figure 2, the thin-wire wave (√(E/ρ) speed can be calculated (figure 3). (Note: if the relation between Young's modulus and raw stock diameter is truly linear, then the thin-wire wave speed can't also be linear since it involves the square root of the modulus. However, the deviation from linear is insignificant over the range of interest.)

Data scatter

The data scatter shown in figure 2 is, unfortunately, not unusual for titanium. Figure 4 (from TIMET, p. 14) shows the variation in Young's modulus for eight heats of Ti‑6Al‑4V sheet, both in the longitudinal and transverse material directions. At room temperature the data scatter for both material directions is approximately ± 2.8 GPa.

(From an orthotropic perspective, on average Young's modulus in the transverse direction (~118 GPa) is about 5% higher than in the longitudinal direction (~107 GPa) at room temperature.)

In the above chart, WQ = water quenched; AC = air cooled.

Data from Culp for an undisclosed titanium alloy (forged) show that Young's modulus can even vary along the length of a single bar. In these tests, the drive and pickup were both electrostatic so there was no attached transducer to contaminate the results.

Repeated tests show that the data are very repeatable. Thus, the variation in Young's modulus along the bar must be due to actual variations in the material properties rather than testing errors.

Interestingly, Young's modulus for this material is higher in the longitudinal direction than in the long transverse direction. However, this conflicts with other known data for this material.

Plate stock

Since titanium is orthotropic, different moduli may be expected in each of the three material directions (longitudinal, transverse, short transverse). Although this information undoubtedly exists (aircraft manufacturers), it does not seem to be publically available.

Culp has compiled data for horns whose longitudinal material direction is parallel to the principal direction of vibration (the stud axis). The procedure and data are given in Appendix A. Excluding the one outlier at 132.4 GPa, the average modulus is 119.6 GPa. Except for one outlier the data scatter is reasonable and does not appear to depend on the horn's thickness.

Poisson's ratio

A wide range of values have been reported for Poisson's ratio. These values are affected by the same factors as the wave speed and modulus (above).

  • "It is difficult to give a reliable value for Poisson's ratio for titanium alloys since anisotropy leads to small differences in both elastic and shear moduli which, when taken together to calculate Poisson's ratio, can lead to values varying from 0.287 to 0.391 for annealed ASTM Grade 5 (Ti-6%Al-4%V) sheet. However, the generally accepted value for commercially pure titanium is 0.36 and that for ASTM Grade 5 is 0.31." (AZO Materials)
  •  "Poisson's ratio depends on material texture and measurement directions. Ten observations at TIMET, using a two element rosette strain gage, gave a mean value of 0.342 with a range of observations from 0.287 to 0.391." (TIMET, p. 15)
  • Culp
    • 76 mm x 76 mm plate material - nodal amplitude measurements zzz
    • Spool horn face U measurements zzz

Fatigue

Fatigue curves show mean failures (i.e., for a given stress, the life at which 50% would have survived but 50% would have failed). However, in practice a 50% failure rate would not be acceptable. Therefore, the stress must be reduced in order to obtain acceptable life with a reasonable failure rate (perhaps <5% ). The question is by how much the stress must be reduced.< p>

In addition, laboratory fatigue (S‑NL) tests are conducted under highly controlled ("ideal") conditions. (Here, laboratory fatigue tests are designated as S‑NL to distinguish them from fatigue results that occur under real-world conditions. The S‑NL tests use carefully prepared specimens at relatively low frequencies - typically around 30 Hz. Such tests are sometimes referred to as Wӧhler tests after the early German investigator. See Juvinall, pp. 205 - 206.) When using S‑NL data to estimate the fatigue of a resonator, care must be taken to assure that the conditions are the same. Otherwise, the fatigue estimate for the resonator would need to be adjusted compared to the S‑NL data. This often results in a reduction in the estimate of allowable resonator stress. The following factors should be considered when comparing real-world fatigue to S‑NL data and when interpreting S‑NL graphs.

  1. Surface finish. S‑NL test specimens typically have a finely polished surface finish, often parallel to the specimen's axis. Horns would not normally receive such care so their lives could be shorter than the S‑NL test specimens at the same stress level.
  2. Surface treatments. Surface treatments include platings and shot peening (which may be beneficial under certain circumstances).
  3. Stress concentration. S‑NL test specimens are often machined with notch to give a specific stress concentration. This will be indicated if the sterss concentration factor Kt is greater than 1.0.
  4. Machining. The horn may have machining defects (e.g., unblended radii) that are not present in the S‑NL specimen. If these defects are present in a highly stressed region then the allowable stress would have to be reduced.
  5. Test direction. Fatigue may be sensitive to the grain direction. See below.
  6. Frequency. Ultrasonic fatigue tests often show reasonable agreement with conventional low-frequency S‑NL fatigue tests (see below for an example) but this issue is not completely resolved. See Wells. Also see Neppiras (2) (p. 707) who states, "Measurements have confirmed that the fatigue limit is a function of the operating frequency [comparing ultrasonic results to low-frequency tests]." (Note, however, that this statement does not specifically refer to titanium.)
  7. Test mode. Rotating beam and reversed bending tests allow higher stresses than axial tests because the interior of the S‑N specimens does not see the full surface stress. Unlike axial fatigue specimens, The stresses in rotating beam and bending specimens are highest on the surface and reduced stressed in the interior. Therefore, these specimens may allow higher stresses than axially stressed specimens where the stresses are uniform across the cross-section. Therefore, to account for axial loading Juvinall (p. 231) suggests reducing the the endurance limits S'n of rotating beam and reversed bending tests by about 10%.
  8. Size. Larger parts generally allow lower stresses because there is more material (and potention defects) from which fatigue cracks may start. See Juvinall (p. 231).
  9. Material's processing (forged, extruded, rolled, etc.). See below.
  10. Material shape (rod, bar, plate, sheet)
  11. Heat treatment. Titanium's heat treated titanium will affect the endurance limit. For example, matweb.com gives 240 MPa for generic annealed Ti–6Al–4V at 107 cycles (matweb‑1) versus 160 MPa for STA (solution treated and aged) (matweb‑2). (Important: the test conditions were not specified. Therefore, these endurance limits should only be used for comparison.)
  12. Residual stresses. Residual tensile stresses may reduce the fatigue life. On the other hand Donachie (p. 177) notes, "One further observation about titanium alloys is that fatigue data reported in the literature often may be on material with favorable surface residual stress induced by turning, milling, etc. Fully stress-relieved or chem-milled surfaces probably have fatigue strengths below the reported alloy capabilities, because the latter have been biased upward by the favorable - that is compressive - stresses."
    Note that some machining operations (e.g., harsh electro-discharge machining EDM (discussed elsewhere)) can induce high residual tensile stresses.
  13. Static stresses. The allowable ultrasonic stress will be reduced when compressive static stresses are present. Such stresses can be significant when long medical probes are loaded transversely at the free end. (Static tensile stresses have no effect on fatigue.)
  14. Environment. Adverse environmental factors (temperature, corrosives, cavitation) may reduce the allowed stress. Note that elevated temperatures may arise from heat that is generated within the resontor material due to the ultrasonic vibration (i.e., hysteresis type heating) and from heat that is generated by the ultrasonic process (e.g., heat that is transferred from the melted plastic to the horn's face).

Effect of grain direction

Fatigue may be affected by direction of the grain relative to the principal stress. For example, see graph of Boyer (p. 431) below. (The test mode was rotating-cantilevered.) Note that, unlike Bowen above, the longitudinal direction has considerably longer life than the long transverse direction.

Effect of processing

Fatigue may be affected by how the material is processed. Figure 6 (Willertz, p. 341) shows this effect for fine grained α‑β, tested in pure water, where the lamellar performed significantly better than the equixed. The test samples were round so the material is not sheet but other information is not available. (Note, in this case, the general agreement between the results at conventional and ultrasonic frequencies.)

Other titaniums

Ti‑7Al‑4Mo

Branson uses Ti‑7Al‑4Mo (7% aluminum, 4% molybdenum), typically from TIMET. Branson switched from Ti‑6Al‑4V in the early 1970's:

  1. During the development of their ultrasonic metal welder, the steel welding ring (in the region of the welding lobe) would eventually cause the adjacent horn interface to deteriorate. Ti‑7Al‑4Mo seemed to give improved life.
  2. Ti‑7Al‑4Mo seemed to reduce the variability in tuned lengths (i.e., a more consistent modulus).

The literature suggests that this material may have higher fatigue strength than Ti‑6Al‑4V. However, this material may be difficult to obtain in small quantities.

Ti‑6Al‑4V‑2Sn

Wuchinich (3) found that this material survived repeated operation at 6 million ultrasonic cycles at 414 MPa with water cooling. Notes:

  1. The sample was annealed for one hour at 700 °C followed by air cooling.
  2. A single sample was tested so additional tests may be warranted.
  3. Young's modulus was measured as 99.3 GPa. Thus, this material will tune somewhat shorter than Ti‑6Al‑4V whose modulus for this size is ~107 GPa.

Machining

When available, carbide tools are recommended. Ample cooling/cutting fluid must be applied. Small diameter taps require extra care because titanium tends to seize the tap which can cause the tap to break. Tapfree is a good cutting fluid for this situation.

Details ...

Recommendations

  1. For consistency of material properties, always order material from the same vendor and, preferably, from the same manufacturer.
  2. Always specify the grain direction on the resonator drawing.
  3. Because most rectangular horns can be machined from plate stock but some rectangular horns are too large for bar stock, plate stock should be used where possible for rectangular horns to assure consistency.
  4. Where the material dimensions permit, cylindrical horns should be machined from cylindrical stock rather than plate stock. This is because, although the material properites may vary radially, there should be little variation circumferentially so the amplitude variation at any given radius should be minimized. (If the horn were machined from plate stock with the stud axis in the thickness (short transverse) direction, then the amplitude at a given radius could vary due to differences in the plate's properties in the longitudinal and long-transverse material directions, both of which are transverse to the stud axis.)
  5. In order of preference, the grain direction (relative to the resonator's principal stress direction) should be specified as: 1) short transverse, 2) longitudinal, 3) long transverse. However, short transverse may not be available in sufficient size.
  6. For Ti‑6Al‑4V:
    1. Use annealed material because it has better fatigue and lower loss than STA material.
    2. For horns that are machined from cylindrical stock, Young's modulus may be taken from figure 2.
    3. For horns that are machined from plate stock where the the grain direction parallel to the principal direction of vibration, 119.6 GPa ia a reasonable first estimate for Young's modulus.
    4. Considering the many variables involved in fatigue, then for annealed Ti‑6Al‑4V whose principal vibration is parallel to the longitudinal grain direction, the literature and experience suggest that (as a rough rule of thumb) the maximum peak alternating stress should not exceed 350 MPa (50 kpsi) under normal conditions (reasonable surface finish, no residual stress, no corrosives, etc.), assuming essentially infinite life is needed. Special circumstances may allow a higher or require a lower peak alternating stress.

Appendix A
Young's Modulus for Ti‑6Al‑4V Plate Material

Longitudinal grain direction

A series of horns was machined with the grain direction parallel to the principal direction of vibration. Each horn was analyzed with FEA whereby Young's modulus was adjusted until the FEA frequency agreed with the actual horn's measured frequency. Young's modulus was thus determined as though the material were isotropic although the material is likely orthotropic.

Notes:

  1. All horns are bar horns.
  2. Horn dimensions are listed as "face width" x "face thickness" x "back thickness".
  3. All dimensions are rounded to the nearest mm.
  4. TIMET is a titanium manufacturer. President Titanium is a vendor that supplies titanium from various sources.
  5. The 35 kHz 83 mm x 5 mm x 23 mm horn has a modulus of 132.4 GPa. This appears to be an outlier. If this datum is excluded then the average modulus changes to 119.6 GPa (–0.5%).
  6. With this type of test, the attached transducer may have some effect on the frequency and, hence, on the determined modulus.
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