LPT Blade & Disc Design - Part 2
Low-Pressure Turbine Blade & Disc Design
Full Engineering Study – Part 2: Structural Analysis in ANSYS Mechanical
Carlos Muñoz Serrano – Mechanical & Project Engineer
1. Introduction
This document is the second part of the engineering study of the low-pressure turbine (LPT) blade and disc presented in Part 1. While Part 1 developed the CAD modelling of the rotor in CATIA V5, this part addresses its structural validation under simulated operating conditions using ANSYS Mechanical.
The objective is to evaluate the mechanical behaviour of the blade under the centrifugal load associated with the reference operating point of the Orenda Mark 14 (7,800 rpm), to identify the critical stress zones, and to assess the fatigue life of the component against high-cycle fatigue (HCF) and low-cycle fatigue (LCF) mechanisms.
As in Part 1, the analysis follows an industrial-style methodology, remaining transparent about the simplifications required by the lack of proprietary data. Every hypothesis, material model, and boundary condition, mesh density, is stated and justified explicitly, rather than left implicit.
2. Geometry and Model Preparation
2.1 Geometry recap
The geometry analysed corresponds to the LPT blade developed in Part 1: NACA 6412 aerodynamic profile (50 mm root chord, 150 mm height) mounted on a three-lobe fir tree root (base 60 × 24.4 mm, θ = 38°, α = 75°, β = 12°, d = 3 mm, r_valley = 2 mm) with a 7° axial draft angle. The blade is free-standing, without a shroud.
2.2 Geometry repair for meshing
The CATIA solid was exported and imported into ANSYS SpaceClaim for clean-up prior to meshing. This step is standard industrial practice: CAD surfaces designed for visual and manufacturing purposes often contain small gaps, residual slivers, or non-manifold edges that prevent a clean volumetric mesh. In this case the imported solid had very few issues; only the trailing edge fillet was rebuilt, since it was causing meshing problems.
3. Material
3.1 Material selection
Inconel 718, a nickel-chromium superalloy, has been selected as the blade material. It is the reference material for LPT blades and discs in this thrust and temperature class, combining good strength retention at high temperature and good fatigue behaviour under cyclic centrifugal loading, which makes it the appropriate reference material even though the exact alloy used in the Orenda Mark 14 is not publicly documented.
3.2 Constitutive model
A Bilinear Isotropic Hardening model has been used to represent the elastoplastic behaviour of the material, rather than a purely linear-elastic model. This choice allows the simulation to capture local plastic yielding at stress concentration zones, such as the fir tree valley and the trailing edge–platform transition, without producing artificially unbounded stress values in regions where the material would, in reality, yield and redistribute load.
| Property | Value |
|---|---|
| Yield strength (Sy) | 1100 MPa |
| Tangent modulus | 2655 MPa |
| Hardening model | Bilinear Isotropic Hardening |
| Young's modulus (E) | 200,000 MPa |
Table 1 — Mechanical properties of Inconel 718 used in the model (Bilinear Isotropic Hardening).
3.3 Note on material data provenance
The mechanical properties used correspond to wrought Inconel 718 rather than additively manufactured material. This is an explicit simplification: wrought properties are well characterised and widely published, whereas AM Inconel 718 properties depend strongly on process parameters and post-processing (HIP, heat treatment) that are outside the scope of this project. The wrought dataset is therefore used as the representative, conservative reference.
4. Finite Element Model
4.1 Mesh
The blade was discretised using 10-node tetrahedral elements (Tet10). Second-order tetrahedral elements were chosen for their ability to capture curved geometry, particularly the fir tree fillets and the aerodynamic surface, without the meshing difficulty associated with hexahedral elements on this type of geometry.
4.2 Mesh density
The analysis was run under a commercial ANSYS licence, so there is no limitation on the number of nodes or elements such as the one imposed by a student licence. The mesh density finally adopted therefore responds purely to a criterion of accuracy and computational cost: local refinement at the fir tree root and at the trailing edge–platform transition, identified from the outset as the zones most likely to show stress concentration, while keeping a coarser mesh on the aerodynamic surface away from the root, where stress gradients are lower.
4.3 Mesh convergence study
A mesh convergence study was carried out at the critical trailing edge–platform transition to confirm that the stress concentration observed there is a genuine geometric effect (a real Kt) and not a meshing artefact. Progressive local refinement was applied at this location across several mesh density levels, recording the peak equivalent stress at each step.
The stress value stabilised as the mesh was refined, converging towards the reported peak of approximately 1,060 MPa rather than continuing to grow unbounded (the behaviour characteristic of a genuine stress concentration as opposed to a singularity). This result was the basis for keeping the design as-is rather than treating the peak as numerical noise, and is discussed further in Section 6.
| Mesh size | Nodes | Elements | σ_max (MPa) |
|---|---|---|---|
| 3 | 19,817 | 11,893 | 948 |
| 2 | 56,088 | 36,185 | 1,072 |
| 1 | 507,639 | 340,656 | 1,060 |
Table 2 — Mesh convergence study.
4.4 Element Quality
In addition to the convergence criterion described in Section 4.3, the geometric quality of the mesh was verified using the ANSYS Mechanical Element Quality metric, which combines the ratio between element volume and edge length into a value normalised between 0 (degenerate element) and 1 (ideal regular element).
The Mesh Metrics histogram (Fig. 1) shows that most elements fall in the 0.8–1 range, indicating a mesh predominantly made up of highly regular tetrahedra, with very few distorted elements. This result is consistent with the use of second-order Tet10 elements on a geometry previously repaired in SpaceClaim (Section 2.2), which removes problematic faces and edges before meshing.
A high mesh quality in the critical zones (the fir tree root and the trailing edge–platform transition) reinforces the reliability of the stress results obtained in those zones, since it rules out the observed stress peaks being a consequence of poorly formed elements, in line with the conclusion already reached in the mesh convergence study.
Fig. 1 — Element Quality histogram of the mesh (most elements between 0.8 and 1).
Fig. 2 — Detail of the Tet10 mesh at the fir tree root and the platform.
5. Boundary Conditions and Loads
5.1 Load: centrifugal rotation
The blade was subjected to a rotational speed of 7,800 rpm about the X axis, matching the reference operating point of the Orenda Mark 14. This load generates the centrifugal body-force distribution that dominates the stress state of a free-standing LPT blade, and is the main loading mechanism governing both the stress peak at the trailing edge–platform transition and the root stresses relevant to fatigue.
5.2 Load: internal gas-flow pressure
In addition to the centrifugal load, a pressure of 0.1 MPa was applied on the inner surface (suction/pressure side exposed to the flow) of the blade, representing the static aerodynamic load exerted by the exhaust gas flow on the aerofoil at the operating point considered. Although small in magnitude compared with the centrifugal load, this pressure contributes to blade bending and is included in the static model so that the resulting stress state is representative of the actual combination of loads in service, rather than of the rotational effect alone.
5.3 Root support condition: from Fixed Support to Compression Only Support
The fir tree root was initially constrained using a Fixed Support applied on the flank faces. This first approach produced numerical singularities at the contact edges of the fir tree flanks: since a Fixed Support prevents any displacement on the constrained faces, mesh-dependent stress peaks appeared exactly at the geometric contact edges, a known artefact of over-constraining what is in reality a contact condition with a rigid support.
A Compression Only Support was adopted as the final boundary condition. Physically, the fir tree flanks only ever transmit load in compression (they can never pull the disc slot towards them), so a Compression Only Support represents the real unilateral contact behaviour of the joint far more faithfully than a Fixed Support, while also removing the artificial singularities introduced by the fully rigid constraint.
Fig. 3 — Load and support setup with Fixed Support on the fir tree flanks.
Fig. 4 — Von Mises stress in the fir tree with Fixed Support: numerical singularity at the contact edges (up to 655 MPa).
Fig. 5 — Load and support setup with Compression Only Support on the fir tree flanks.
Fig. 6 — Von Mises stress in the fir tree with Compression Only Support: realistic distribution without singularities (180–205 MPa).
6. Results — Static Structural Analysis
6.1 General stress distribution
Under the combination of the centrifugal load and the 0.1 MPa pressure applied on the inner surface, the von Mises stress distribution is reasonably well balanced along the blade. The fir tree, despite reacting the entire centrifugal load through its flanks, shows low stress levels, indicating an adequate sizing of the root. The rest of the aerodynamic span likewise shows moderate stresses, with no significant concentrations other than in the zone identified in Section 6.2.
Fig. 7 — General von Mises stress distribution across the full blade (peak of ≈1,060 MPa at the trailing edge).
6.2 Critical zone: trailing edge–platform transition
The maximum stress in the model, approximately 1,060 MPa, occurs at the geometric transition between the trailing edge and the platform. As established by the mesh convergence study in Section 4.3, this peak is a confirmed geometric effect and not a numerical artefact. This point also shows the highest plastic strain, at 0.0053464 mm/mm.
Fig. 8 — Detail of von Mises stress at the trailing edge–platform transition (critical zone).
Fig. 9 — Equivalent plastic strain in the critical zone (Δεp max. = 0.0053464 mm/mm).
6.3 Design decision
Given that the peak stress is a confirmed geometric effect and not a meshing error, the decision adopted was to keep the current design as-is and document the finding as a conclusion of this study, rather than undertaking an immediate redesign. Two possible mitigation routes have been identified as recommended future work, without implementing them in this study:
- Increasing the fillet radius at the trailing edge–platform transition, to reduce the stress concentration factor (Kt) at that point.
- Reducing the height of the aerodynamic surface, which would reduce the lever arm through which the internal pressure acts on the blade base, reducing the induced bending moment and, with it, the resulting stress at the transition.
It should also be noted that the 0.1 MPa pressure load has been modelled as a uniform pressure on the inner surface of the blade, a relevant simplification. In service, the loads exerted by the gas flow on the aerofoil would not be uniform, but would depend on the real aerodynamic pressure distribution along the chord and span (normally obtained via CFD). This simplification may therefore have overestimated or artificially shifted the observed stress concentration, so the result should be interpreted as a conservative approximation rather than an aerodynamically validated load distribution.
This reflects how a finding of this kind would typically be handled in an early design review: an identified risk with several proposed mitigations and the limitations of the load model explicitly documented, rather than an unplanned late-stage geometry change based on a simplified load.
6.4 Extracted numerical results (Probes)
Once the geometric nature of the stress peak was confirmed, the numerical values of mean stress (σm) were extracted via Probes at the two critical points identified (trailing edge and fir tree valley) together with the equivalent plastic strain (Δεp) at the trailing edge. These values are the input basis for the fatigue calculation developed in Section 8.
| Magnitude | Value | Remark |
|---|---|---|
| σm trailing edge (converged) | 1,060 MPa | Very close to the nominal yield strength (Sy = 1,100 MPa) |
| σm fir tree valley | 306 MPa | Well below Sy — safe zone |
| Δεp trailing edge (Equivalent Plastic Strain) | 0.0053464 mm/mm | Confirms localised plastic yielding at the stress concentration peak |
Table 3 — Mean stress and plastic strain extracted via Probes at the critical points of the static analysis.
The non-zero equivalent plastic strain at the trailing edge confirms that local plastic yielding exists at that point, even though the mean stress extracted by Probe (1,060 MPa) sits slightly below the nominal yield strength of the material: the yielding is highly localized, consistent with a stress concentration peak of reduced extent, and does not represent generalised yielding of the section.
7. Modal Analysis
7.1 Approach
Following the static structural analysis, a prestressed modal analysis was carried out, using as the starting state the steady condition under the 7,800 rpm centrifugal load and the 0.1 MPa pressure load. The stress-stiffening effect associated with rotation is thereby incorporated into the blade stiffness before extracting the natural frequencies, rather than computing an unloaded modal analysis, which would underestimate the real operating frequencies.
7.2 Frequencies and mode shapes
The first natural modes of the blade were extracted, corresponding to the vibration mechanisms expected in a free-standing blade: weak-axis bending, strong-axis bending, and torsion. These mode shapes serve as a reference for assessing the risk of resonance against the engine's excitation frequencies (Engine Orders).
Fig. 10 — First mode shape of the blade (Mode 1, f₁ = 797.16 Hz).
7.3 Relation to the Campbell diagram
The Campbell diagram, which would cross these natural frequencies with the engine's Engine Order lines at different rotational speeds, has been deliberately excluded from this study because real Engine Order data for the Orenda Mark 14 is not available. The modal analysis presented here lays the groundwork (frequencies and mode shapes) for building that diagram should such information become available in the future, thereby avoiding the fabrication of unverifiable input data.
| Mode | Frequency (Hz) |
|---|---|
| 1 | 797.2 |
| 2 | 2,441.3 |
| 3 | 3,206.7 |
| 4 | 3,732 |
| 5 | 6,225.5 |
| 6 | 7,922.7 |
| 7 | 10,656 |
| 8 | 12,288 |
| 9 | 12,809 |
| 10 | 13,345 |
Table 4 — Natural frequencies of the first 10 modes of the blade (prestressed modal analysis).
7.4 Resonance check
At a rotational speed of 7,800 rpm (f_rot = 130 Hz), it was verified that no mode falls into exact resonance with an integer Engine Order. The mode closest to an Engine Order line is Mode 1 (797.2 Hz), close to EO6 (6 × 130 Hz = 780 Hz), with a +2.2% separation. This separation, while not eliminating the risk of forced vibration, indicates that the design operating point is not in direct resonance, and is used as engineering justification in the estimation of the alternating stress for the HCF fatigue calculation (Section 8.3).
8. Fatigue Analysis
8.1 Two distinct fatigue phenomena
The blade is subject to two fatigue mechanisms of a different nature, which require distinct calculation methods and answer different questions.
High-cycle fatigue (HCF) — vibration during steady-state operation
While the engine runs at a constant regime (7,800 rpm), the background stress in the blade (due to the centrifugal load and the flow pressure) is practically constant in time. However, the blade does not pass through a perfectly uniform flow: as it repeatedly passes near the stator vanes and non-uniform flow regions, it receives small periodic high-frequency excitations superimposed on that background stress. This is the alternating stress (σa) that enters the Goodman criterion.
The Goodman criterion does not compute a number of cycles or hours: it is an infinite-life criterion. It compares the operating point (σm, σa) of the blade with the material's Goodman line and gives a binary verdict: if the point falls inside the envelope, the blade is considered to withstand this vibration indefinitely without fatigue failure; if it falls outside, it is considered to fail within a relatively low number of cycles, although the criterion itself does not state how many.
With the data available in this study, no real value of σa is available (no harmonic response analysis with real Engine Order data has been carried out), so σa has been estimated as a percentage of σm. This limitation prevents translating the Goodman result into a concrete figure of operating hours: it only allows establishing whether, under the assumed σa hypothesis, the blade is inside or outside the infinite-life condition against vibration.
Low-cycle fatigue (LCF) — start-stop cycles
Unlike the previous mechanism, here the load cycle is real and of large amplitude: every time the engine starts, the rotational speed goes from 0 to 7,800 rpm, and back to 0 when it stops. This constitutes one full centrifugal load cycle per engine start-stop, not per rotor revolution or per flow perturbation.
The Coffin-Manson method relates the plastic strain generated in each of these cycles to the number of cycles the material withstands before crack initiation. Unlike Goodman, this method does provide a concrete figure: the value of N obtained (≈779 cycles) is the number of start-stops the blade withstands at the critical point, and can be translated into a life estimate in years if the engine's usage frequency (starts per year) is known.
In summary: Goodman assesses whether the blade withstands high-frequency vibration indefinitely during steady-state operation (without being able to quantify hours with the current data), while Coffin-Manson quantifies how many start-stop cycles the blade withstands before failure. Both analyses are necessary because they cover independent, non-substitutable damage mechanisms.
8.2 Calculation methodology
The fatigue calculation was not performed using the Fatigue Tool module built into ANSYS, but manually in a spreadsheet (Excel), based on the stresses extracted from the model via Probes at the identified critical points (trailing edge–platform transition and fir tree valley). This manual approach was prioritised over the automated one for transparency: it allows every hypothesis and formula used at each step of the calculation to be made explicit, rather than relying on a black box.
A dedicated fatigue calculator was developed for this project, organised into four sheets: Executive Summary (overall status and notes on the simplifications adopted), Input Data (material properties and stresses extracted from ANSYS), Goodman HCF (high-cycle fatigue calculation), and Coffin-Manson LCF (low-cycle fatigue calculation). The material values used in Section 3.2 and in the following calculations — Su, Sy, Se, E, ε'f, and c — correspond directly to the Input Data sheet of this calculator.
The Goodman HCF sheet also includes a Goodman diagram with the criterion line and the operating points of the two critical zones superimposed (trailing edge at σa=15% and σa=10%, and the fir tree valley), together with a sensitivity-analysis block that recalculates the FoS under the alternative σa hypothesis. The Coffin-Manson LCF sheet includes the material's cyclic ductility curve with the real operating point of the trailing edge marked on it.
8.3 High-cycle fatigue (HCF) — Goodman method
For high-cycle fatigue, the Goodman criterion is used, combining the mean stress (σm) and the alternating stress (σa) at each critical point with the ultimate strength (Su) and the fatigue limit (Se) of the material, to obtain a factor of safety (FoS) against high-cycle fatigue failure. Su = 1,375 MPa and Se = 500 MPa have been used, the latter conservatively estimated as Se ≈ 0.36 × Su, in the absence of a published fatigue-limit value specific to this condition of Inconel 718.
As no real aerodynamic excitation data is available (a harmonic response analysis with real Engine Orders would be required), the alternating stress is estimated as a percentage of the mean stress (σa = %·σm), a common hypothesis when the real vibratory amplitude is unknown. The higher this percentage, the more conservative the result: it is assumed that the blade vibrates more than it probably does in reality, and the point moves further from the Goodman line.
A base value of 15% is used, the usual conservative hypothesis when no additional information on the blade's dynamic behaviour is available. However, the modal analysis (Section 7.4) provides that additional information: Mode 1 sits 2.2% above EO6, i.e. the blade does not operate at exact resonance. Since the amplitude of a forced vibration drops rapidly away from resonance, a lower vibratory response than the generic worst case can reasonably be expected, which justifies also evaluating a 10% case. This is, in any case, a qualitative argument — the modal analysis confirms the absence of resonance but does not quantify the real amplification factor — so both results are presented in parallel rather than one replacing the other.
| Critical zone | σm (MPa) | σa (MPa) | σa limit (MPa) | FoS HCF |
|---|---|---|---|---|
| Trailing edge (σa=15%) | 1,060 | 159 | 114.5 | 0.72 — outside Goodman |
| Trailing edge (σa=10%) | 1,060 | 106 | 114.5 | 1.08 — inside Goodman |
| Fir tree valley (σa=15%) | 306 | 46 | 388.7 | 8.47 — ample margin |
Table 5 — Result of the Goodman (HCF) criterion at the critical zones, under the two σa hypotheses evaluated.
The result at the trailing edge is therefore sensitive to the σa hypothesis adopted: with the generic 15% the point falls outside the Goodman diagram, while with the 10% justified by the modal separation it falls inside. The fir tree valley shows an ample margin under either hypothesis.
8.4 Low-cycle fatigue (LCF) — Coffin-Manson method
For low-cycle fatigue, associated with the engine's start-stop cycles, the Coffin-Manson relation is used, relating the cyclic plastic strain (Δεp) extracted from the model to the material's cyclic ductility parameters (ε'f = 0.22, c = −0.60) to estimate the number of cycles to crack initiation at the trailing edge.
| Step | Value |
|---|---|
| Δεp extracted from ANSYS | 0.0053464 mm/mm |
| Δεp / 2 | 0.0026732 |
| (Δεp/2) / ε'f | 0.01215 |
| Exponent 1/c | −1.6667 |
| 2N | 1,558 |
| N — cycles to failure | 779 cycles |
Table 6 — Coffin-Manson (LCF) calculation steps leading to the number of cycles to failure.
Assuming an estimate of 200 start-stop cycles per year, the 779 cycles obtained correspond to an estimated life of approximately 3.9 years at the critical point of the trailing edge. This is a conservative result, since the plastic strain concentration occurs in a zone of reduced extent (stress gradient effect), so the Coffin-Manson method applied directly, without gradient correction, tends to penalise the estimated life.
9. Discussion and Limitations
The following simplifications and hypotheses have been assumed throughout the study and should be taken into account when interpreting the results:
- Isothermal analysis at 20°C: the real operating thermal gradient has not been modelled, which in a real LPT affects both the material properties and the stress state.
- The alternating stress (σa) used in the HCF calculation is an estimate as a percentage of σm, not a value obtained from a harmonic response analysis with real aerodynamic excitation.
- The root boundary condition (Compression Only Support) is a simplification of the real disc-blade contact, which in service includes friction and possible fretting.
- The stress concentration at the trailing edge is of reduced extent (stress gradient), which conservatively penalises the Coffin-Manson calculation applied without gradient correction.
- The Campbell diagram has been excluded due to the lack of real Engine Order data for the Orenda Mark 14; the modal analysis carried out lays the groundwork to complete it should that data become available.
10. Conclusions
| Aspect | Result |
|---|---|
| Peak stress (trailing edge–platform) | σm = 1,060 MPa (converged Probe) |
| Nature of the peak | Geometric (real Kt), confirmed by convergence study |
| Local yielding | Confirmed (Δεp = 0.0053464 mm/mm), localised in nature |
| Fir tree valley zone | Safe, σm = 306 MPa, FoS HCF = 8.47 |
| Modal resonance | Absent; Mode 1 at +2.2% from EO6, no exact match |
| FoS HCF trailing edge | 0.72 (σa=15%, generic) / 1.08 (σa=10%, justified by modal separation) |
| LCF life, trailing edge | 779 cycles (~3.9 years at 200 cycles/year), conservative estimate |
Table 7 — Summary of the main results of the structural, modal, and fatigue study.
The study confirms that the trailing edge is the critical zone of the blade both in static stress and in fatigue, while the fir tree valley shows an ample margin under all conditions evaluated. The absence of exact modal resonance with integer Engine Orders supports the more favourable σa hypothesis (10%), under which the critical point falls inside the Goodman criterion; however, under the more conservative generic hypothesis (15%) the same point falls outside, underlining the sensitivity of the result to the real aerodynamic excitation, which is not available in this study. The LCF life estimate (~3.9 years) is a conservative result and should be interpreted as a lower bound, conditioned by the uncorrected stress-gradient effect.
11. Recommended Future Work
- Increase the transition radius at the trailing edge to reduce the stress concentration factor (Kt).
- Carry out a coupled thermomechanical analysis, incorporating the real operating thermal gradient.
- Build the Campbell diagram with real Engine Order data for the Orenda Mark 14.
- Carry out a harmonic response analysis to obtain a real value of σa, instead of the estimate as a percentage of σm.
- Model the blade-disc assembly with frictional contact, instead of the simplified Compression Only Support.
- Apply fatigue criteria with stress-gradient correction (Neuber, Peterson) to refine the estimated LCF life in stress concentration zones of reduced extent.
12. Resources and References
- Special Metals Corporation — Inconel 718 datasheet.
- ASM Handbook, Volume 19 — Fatigue and Fracture.
- Suresh, S. — Fatigue of Materials.
- Bannantine, J. A. — Fundamentals of Metal Fatigue Analysis.
- ANSYS Mechanical User's Guide, 2026 R1.
- Technical and photographic documentation of the Orenda Mark 14.
- Fatigue calculator spreadsheet developed specifically for this project (sheets: Executive Summary, Input Data, Goodman HCF, Coffin-Manson LCF).