## Abstract

Hair fibre failure analysis is an established method to assess fibre damage and the effects of repair processes and products. The tests are generally conducted in two principal ways, either applying cyclic constant stress or strain. Primary results are the number of cycles (N) until fibres in a sample break. The overall results for a sample will depend on the applied stress or strain, as well as on sample treatment. Further influences will derive from testing speed, humidity, temperature, etc. The survival performance of fibres in a sample may be analysed by model-free (e.g. Kaplan-Meier Estimator) or model-based approaches.

For our investigation, we conducted constant strain, non-slack failure experiments on virgin and bleached hair, applying strains in the yield region between 2.5% - 35%, (22oC, 55% rh).

For the analysis of the survival profile, a statistically sound function has been chosen, with which a scale (α) parameter also known as characteristic lifetimes, and a shape parameter (β) have been described. When the number of testing cycles (N) has reached α, 63% (=1/e) of fibres in the sample will theoretically have broken. The model-based approach may be associated with the weakest-link theory, where the value of β is a measure for the overall failure characteristics, providing hints of the likelihood for failure.

Our results show that the number of failure classes for fibres decreases rather dramatically with increasing strain. This is expected, because the experiment moves towards the case of a simple tensile-break experiment, where all fibres will have broken during the first cycle. The

parameter α (as ln α) decreases and β increases consistently with strain. The critical strain level at which the failure mode fundamentally changes will be discussed. The model-based approach indeed, permitted the discrimination between different hair qualities with strain, and a suggestion for an optimal operating level suiting this specific investigation will be presented.

In summary, the explored model turns out to be a feasible statistical model-based approach to identify optimum experimental conditions to assess hair fibre damage in a non-slack constant strain failure experiment. So, that tools can be of potential in improving the reliability of fatigue tests, and once refined in extent for claims support.

For our investigation, we conducted constant strain, non-slack failure experiments on virgin and bleached hair, applying strains in the yield region between 2.5% - 35%, (22oC, 55% rh).

For the analysis of the survival profile, a statistically sound function has been chosen, with which a scale (α) parameter also known as characteristic lifetimes, and a shape parameter (β) have been described. When the number of testing cycles (N) has reached α, 63% (=1/e) of fibres in the sample will theoretically have broken. The model-based approach may be associated with the weakest-link theory, where the value of β is a measure for the overall failure characteristics, providing hints of the likelihood for failure.

Our results show that the number of failure classes for fibres decreases rather dramatically with increasing strain. This is expected, because the experiment moves towards the case of a simple tensile-break experiment, where all fibres will have broken during the first cycle. The

parameter α (as ln α) decreases and β increases consistently with strain. The critical strain level at which the failure mode fundamentally changes will be discussed. The model-based approach indeed, permitted the discrimination between different hair qualities with strain, and a suggestion for an optimal operating level suiting this specific investigation will be presented.

In summary, the explored model turns out to be a feasible statistical model-based approach to identify optimum experimental conditions to assess hair fibre damage in a non-slack constant strain failure experiment. So, that tools can be of potential in improving the reliability of fatigue tests, and once refined in extent for claims support.

Original language | English |
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Title of host publication | Proc TRI 10th Int Conf Applied Hair Science 2022 |

Publisher | TRI - Princeton, NJ, USA |

Volume | 2022 |

Publication status | Published - 8 Jun 2022 |