DOI: 10.5281/zenodo.16895991
title: Multiaxial Simulation data

description: Alloy 709 Multiaxial Creep Simulation Dataset

This dataset contains multiaxial creep simulation results for Alloy 709 generated with a crystal-plasticity finite-element (CPFE) framework. The raw data comprise time-series outputs (out.csv) from approximately 172 simulations at 600, 700, 800, and 900 °C. Each out.csv records creep–damage evolution, including creep strains and strain rates, stresses, the damage parameter D, and derived quantities (e.g., hydrostatic and von Mises stresses).

Directories are organized by temperature and case number (e.g., 600/600-7/out.csv, 700/700-3/out.csv).The case numbering corresponds to stress-state type:



Cases 1–4 → Uniaxial

Cases 5–10 → Biaxial

Cases ≥ 11 → Triaxial




Suffix Definitions


Suffixes in subfolder names further specify the stress mode:



_c → Biaxial/Triaxial compression (pn/pnn)

_c_ppn → Mixed compressive–tensile triaxial (ppn)

_c_pnp → Mixed compressive–tensile triaxial (pnp)

(no suffix) → Tensile states




Curated Rupture Summary


The file tr_results_2.xlsx provides a curated rupture-summary of 80 selected simulations that correspond directly to the multiaxial creep-rupture data reported in Appendix B of the manuscript:

“Development of Predictive Model for Accurate Rupture Time from Multiaxial Creep in Alloy 709 with Physics-Based Simulations.”

Each row lists the stress-state type, temperature, principal stresses (σ₁, σ₂, σ₃ in MPa), and the time-to-rupture (tr, in hours), where tr is extracted from the final simulation time step and converted from seconds to hours.



Note: In the manuscript Appendix, the biaxial and triaxial stress values are presented in rounded engineering form for clarity (e.g., 171.2 MPa, 32.0 MPa, 8.0 MPa).The tr_results_2.xlsx summary table and all out.csv raw time-series files in this dataset retain the full floating-point precision from the CPFE simulations.




Reuse and Applications


These data support reproduction of the paper’s tables and figures and can be reused for:



Benchmarking effective-stress models

Validating invariant-based rupture-life predictions

Developing machine-learning surrogates for multiaxial creep




File Inventory


A709_data/



/600/.../out.csv → Raw creep time series at 600 °C

/700/.../out.csv → Raw creep time series at 700 °C

/800/.../out.csv → Raw creep time series at 800 °C

/900/.../out.csv → Raw creep time series at 900 °C


tr_results_2.xlsx (curated rupture summary, 80 cases)



Column Definitions




tr_results_2.xlsx





Column
Unit
Meaning




case
–
Simulation case identifier (e.g., 12_c_ppn)


T_C
°C
Test temperature


sigma_1, sigma_2, sigma_3
MPa
Principal stresses


tr
h
Time to rupture






out.csv (Raw Time Series)


May include variables such as:



time (s) → simulation time

D (–) → grain-boundary damage (approaches 1 at rupture)

avgcreep_xx, yy, zz → creep strain components

avgstress_xx, yy, zz (MPa) → stress tensor components

sigma_h_max/min (MPa) → hydrostatic stress extrema

sigma_vm_max/min (MPa) → von Mises stress extrema

strain_rate_* (1/s) → instantaneous creep strain rate




Quick Start




Python (pandas)

import pandas as pd

# **Cases 1–4** → Uniaxial  
# **Cases 5–10** → Biaxial  
# **Cases ≥ 11** → Triaxial 

# Set temperature (°C) and case number (1–19)
T = 900
case_num = 12

# Select suffix based on stress state:
# ""        → tensile (uniaxial / biaxial / triaxial, where available)
# "_c"      → compression-dominant triaxial (pnn)
# "_c_ppn"  → mixed triaxial (ppn)
# "_c_pnp"  → mixed triaxial (pnp)
suffix = "_c_ppn"   # <-- change based on case mode

# Construct folder path (after extracting A709_data.zip)
case_folder = f"A709_data/{T}/{T}-{case_num}{suffix}"

# Load raw time-series data
raw = pd.read_csv(f"{case_folder}/out.csv")

# Convert time to hours
raw["time_hr"] = raw["time"] / 3600.0

# Example plot: damage vs time
raw.plot(
    x="time_hr",
    y="D",
    logy=True,
    xlabel="Time (hours)",
    ylabel="Damage D",
    title=f"Damage evolution: case {T}-{case_num}{suffix}"
)