Pressure sensors are based on a measuring body that must be able to tolerate high loading, especially in the high-pressure range. The design and the material used are key factors for the measuring body’s accuracy, reliability, and service life.
The monolithic design of pressure sensors used in the high-pressure range
High-pressure transducers are generally designed as thick-walled tubes (see fig. 1) and are made of a single piece of steel. Therefore, their design is also called “monolithic”. The term “monolithic” is derived from Greek and means “a single stone” (mono- = single; lithos = stone).
The monolithic measuring body design ensures especially low stress gradients and stress peaks. Furthermore, these measuring bodies have a long service life, since they have no weld seams or other weak points. Fig. 2 shows various pressure-hole designs in the schematic layout, while fig. 3 displays a choice of different measuring bodies.
The mechanical stress at the internal diameter Di is significantly higher than at the external diameter Da. Therefore, this is the point subjected to the highest loading due to the triaxial stress state (see fig. 4).
Postulated by strength theory, the reference stress σv must be derived from the three stresses σt (tangential stress), σr (radial stress), and σn (normal stress) to allow an assessment of the service life. The reference stress is then correlated with the material’s characteristic values.
Transducers used in the ultra-high-pressure range (>10,000 bar) are designed such that the material’s yield point is exceeded at the internal fiber, which is subjected to the highest loading. This does not mean that the transducer will be torn apart, since the outer layers of the measuring body still “bear” the pressure very well. If the pressure is increased still further, the place at which the yield point is exceeded moves slowly outward inside the wall. The transducer would only break when the yield point has moved to the outermost layer.
The ratio of internal diameter to external diameter (Da/Di), and thus the thickness of the wall, must be chosen so that the dynamic properties of the spring steel can be fully utilized, and the maximum capacity for load changes is reached.
If cleverly implemented, this design offers the advantage of optimally utilizing the material in terms of its endurance strength values.
Selecting materials involves a compromise between the maximum service life under dynamic loading and the metrological properties that can be achieved by the spring element. Steels that appear to be excellent materials for high-pressure applications due to a high yield point can have unsuitable spring properties that will result in too large a hysteresis. This means that the material will show different characteristic curves for increasing and decreasing stress, which results in measurement inaccuracies. Spring element materials with a low hysteresis have a tensile strength of > 1GPa, which makes them far more suitable for high-pressure applications.
Steels commonly used by pressure transducer manufacturers have a dynamic load-carrying capacity for endurance fatigue of about 600 MPa, which is equivalent to a compressive loading of approximately 6,000 bar. Pressure-bearing parts exposed to repeated loading of 6,000 to 7,000 bar cannot exhibit endurance strength. This is illustrated in fig. 5. The schematic representation of a Wöhler diagram shows the tensile strength Rm as a function of the number of alternating loads and the compressive stress σD.
Low-cycle endurance: Stress amplitudes at which damage (breakage) occurs at N<10³ alternating loads
Static strength: Stress amplitudes at which damage (breakage) occurs at 10³<N<106 alternating loads
Endurance strength: Stress amplitudes at which damage (breakage) does not occur with any number of alternating loads, 2 x 106 ≥ N ≥ 107
Besides the material properties, several other factors influence service life. Furthermore, post-treatment of the transducer also helps ensure that pressure values exceeding 6,000 bar can be reliably measured.
*SG = strain gauge