## 1 Introduction  
Thermal modifications of materials take place in many industrial fields, such as aerospace, chemical industry, nuclear power, electricity, and so on. As a consequence, it is inevitable that the components and structures served especially at elevated temperature could undergo a process of degradation of their properties and performance over time. For example, thermal aging could result in the decrease of the remaining performance life of aluminum alloys utilized in industrial structures and even threaten the security of property and personal safety. Studies have shown that the early performance degradation stage of materials occupied 80-90% of their fatigue life [1; 2; 3]. Therefore, following increasing concerns about safety, the remaining life time and structural health of the materials should be non-destructively monitored with a highest possible sensitivity. Nondestructive evaluation techniques, for instance, X-ray diffraction, acoustic emission, ultrasonic attenuation, and velocity measurement, etc., are implemented for the detection and the characterization of thermal aging and damage in metal materials. In recent years, linear linear ultrasonic techniques have been widely used in the non-destructive testing of physical and mechanical properties of materials [4; 5; 6; 7; 8; 9; 10; 11; 12; 13]. However, acoustic parameter variations measured by linear ultrasonic technology are relatively small in response to early damage and change of materials and structures [14; 15; 16; 17]. Nonlinear acoustic techniques are widely accepted for their higher sensitivity to the state of micro-structured and damaged materials, compared with linear acoustic techniques [14; 17; 18; 19; 20; 21; 22]. In particular, recent studies had theoretically and experimentally confirmed that nonlinear acoustics was an effective and sensitive tool of nondestructive characterization for various thermally treated materials [17; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34]. In comparison with other wave modes used in nonlinear acoustics to detect thermal modification of material state, for example Rayleigh waves [35; 36; 37; 38; 39] and Lamb waves [40; 41; 42; 43], bulk waves [28; 44; 45; 46; 47; 48] were extensively utilized. Although different types of contacting transducers are commonly used to generate and detect acoustic waves in the samples, generation and detection of acoustic waves by lasers is now applied more frequently in non-destructive detection of mechanical and physical properties of the materials. It was demonstrated that interaction between acoustic waves and materials with microstructural changes could be monitored optically [49; 50; 51; 52]. An in-contact but nondestructive method for laser generation of high-amplitude acoustic pulses was developed [53; 54; 55]. In this LSCP (liquid-suspended carbon particles) based method, bulk finite-amplitude longitudinal acoustic waves were generated by the absorption of nanosecond laser pulses in a 50 \(\upmu\)m thick water suspension of carbon particles, deposited on the sample surface. In this paper, we describe the first application of all-optical generation and detection of bulk finite-amplitude longitudinal acoustic waves for measurements of acoustic nonlinearities of aluminum alloys of different thermal aging times. Finite-amplitude acoustic waves were generated on the front surface of aluminum alloy plates by applying the LSCP based method. An optical interferometer was used to detect the out-of-plane displacement of the rear surface of the plate caused by the arrival of laser-generated acoustic pulses. Aluminum alloy plates (Al6061) were heat-treated with different time durations of 0 min, 20 min, 40 min, 1 h, 2 h, 10 h, 100 h, and 1000 h [56]. It was observed that in, all evaluated samples, the duration of detected strain pulses increased with the increase of their amplitude, which is a known manifestation of the hysteretic nonlinearity of the material [57; 58].